# Seminars (CGP)

Videos and presentation materials from other INI events are also available.

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Event When Speaker Title Presentation Material
CGPW01 13th July 2015
09:45 to 10:30
Anotida Madzvamuse Models for growth development in cell motility and pattern formation
The aim of this lecture is stimulate discussions on the development of new theoretical and computational models coupling internal (bulk), surface and external (extra-cellular matrix) dynamics for cell motility and pattern formation. Underpinning this framework are numerous open problems associated with analysis of the models, development of efficient and robust numerical methods as well as fitting models (qualitatively and quantitatively) to experimental observations (data) through optimal control models.
CGPW01 13th July 2015
10:45 to 11:45
Hans Othmer A Theoretician's Overview of Some Basic Problems in the Modelling and Analysis of Cell Motility
CGPW01 13th July 2015
11:45 to 12:30
Group Discusssion
CGPW01 13th July 2015
13:30 to 14:30
Ewa Paluch Actin cortex mechanics in cell migration without focal adhesions
The shape of animal cells is primarily determined by the cellular cortex, a thin network of actin filaments and myosin motors that lies directly underneath the plasma membrane. Cell shape changes are driven by controlled changes in the physical properties of the cortex, which arise from the microscopic architecture, composition and dynamics of the cortical network. We investigate how the mechanical properties of the cortex are controlled at the molecular level, and how changes in these properties drive cell deformation. We have developed methods to investigate the spatial organisation of the cortex at the microscopic scale and are exploring how network organisation and the spatial distribution of motor proteins determine cortical tension. A precise spatial control of cortex tension and contractility is essential during cell shape changes. For example, during cell migration, contractility gradients towards the back of the cell have been involved in promoting cell polarization and the forward movement of the cell body. We are studying the control and function of cortical contractile tension during bleb-based migration of non adherent cells in 3-dimensional confinement. We could show that in such cells, a sustained rearward cortical flow is sufficient to drive persistent cell motion in confinement, even in the absence of specific substrate adhesions. We show that the non-adherent cells use a friction-based migration mechanism, which relies on forces several orders of magnitude smaller than adhesion-based migration. Such focal adhesion-independent locomotion may be advantageous for cells crossing multiple tissues, as it does not require the expression of tissue-specific receptors. Related Links
CGPW01 13th July 2015
14:30 to 15:30
Bernd Hoffmann Migration of epithelial cells
Epithelial cells play a vital role for mechanical integrity at the tissue level by forming a stable cell layer that is connected to the extracellular environment via various cell-cell as well as cell-matrix junctions. However, upon signal induction cells can undergo dramatic morphological changes to switch from a sessile to a highly motile phenotype. Characterized by intense cell polarization a concerted interplay at the level of cytoskeletal dynamics, cell adhesion, force generation, and protein affinity regulation takes place leading to an overall uniform migratory behavior. Although hundreds of molecules and regulatory events are involved, four main steps, namely I) actin polymerization at the cell front, II) adhesion formation, III) cell contraction and IV) de-adhesion at the rear end of the cell characterize the complete motility cycle of epithelial cells making epithelial cells to an ideal model system in order to study basic cell motility events.
CGPW01 13th July 2015
16:00 to 17:00
Group Discussion
CGPW01 13th July 2015
19:00 to 20:00
InCem Come Together
CGPW01 14th July 2015
09:00 to 10:00
Alex Mogilner Design principles of actin lamellipodial treadmill: lessons from the fragment
Co-authors: N Ofer (Technion), D Ben Aroush (Technion), J Allard (UC Irvine), E Abu Shah (Technion), K Keren (Technion)
Actin turnover/treadmill is the central driver of cell migration. Though biochemical players enabling actin treadmill are known, its quantitative understanding is lacking. We focused on lamellipodial fragments form fish keratocytes lacking cell body but retaining the ability to migrate. The geometric simplicity of fragments and the absence of organelles and complex actin structures allowed us to characterize quantitatively the spatial actin organization in motile fragments. We used fluorescent microscopy to measure distributions of actin filaments and monomers, as well as the distributions of barbed ends and pointed ends. We then combined the actin mapping with mathematical modeling and FRAP to understand the organization of the actin turnover and treadmill. We found that more than half of actin is not part of the rapidly turning over F-actin network but is a diffusing fraction of oligomers and monomers, most of which is not available for polymerization. Modeling suggests that such organization of the actin treadmill enables diffusion to recycle actin effectively and makes cell migration steady, yet prepared for rapid focused acceleration.
CGPW01 14th July 2015
10:30 to 11:30
Samuel Safran Physical theories of cell mechanics
Co-authors: Ohad Cohen (Weizmann Institute of Science, Rehovot, Israel), Kinjal Dasbiswas (Weizmann Institute of Science, Rehovot, Israel), Xinpeng Xu (Weizmann Institute of Science, Rehovot, Israel)
Cell contractility at either the coarse-grained level of an entire cell or at the sub-cellular level of individual acto-myosin fibers, can be understood using the concept of elastic force dipoles. These dipoles interact via their mutual deformations of the surrounding visco-elastic medium which can be either the extra-cellular matrix (in the case of cells modeled as force dipoles)  or the internal, cellular cytoskeleton (in the case of acto-myosin fibers within the cell). The theory of these elastically mediated interactions combined with the unique "living" nature of cells (implying that the activity of these dipoles is non-equilibrium and energy consuming) allows us to understand the organization and order of acto-myosin fibers within the cytoskeleton of a single cell or among contractile cells in systems of non-motile and adherent cells. We present the general theory of elastic interactions in the context of acto-myosin activity with examples that demonstrate its utility in understanding experiments on cytoskeletal alignment in stem cells that differentiate  into muscle cells, the structure and beating of cardiomyocytes, very long-ranged cell-cell interactions in fibrous elastic matrices, and elastically controlled diffusion of biomolecules that trigger development in embryos.
CGPW01 14th July 2015
11:30 to 12:30
Group Discussion
CGPW01 14th July 2015
13:30 to 14:30
Till Bretschneider Actin dynamics in Dictyostelium
Dictyostelium discoideum is one of only ten non-mammalian model organisms for biomedical research officially supported by the NIH. Above all this has to do with Dictyostelium being a genetically very tractable organism in general, but particularly in terms of cell migration, signalling to the actin cytoskeleton is remarkably conserved between Dictyostelium and mammalian leukocytes. Furthermore, few other organisms have been studied so extensively regarding theoretical aspects of cell migration. I will review the biology of signalling to the actin cytoskeleton in Dictyostelium, highlighting the role of self-organisation and excitability of the actin system in the formation of functional dynamic structures in the absence of external signals. I will conclude with recent work on image-based modelling of cell reorientation and blebbing. Related Links
CGPW01 14th July 2015
14:30 to 15:30
Alexander Bershadsky Self-organizatin of the actin cytoskeleton

We discuss here some aspects of local and global self-organization of the actomyosin cytoskeleton in the fibroblast-type cells. (1) Locally, the cytoplasm comprises a multi-nodal network formed by small asters of actin filaments nucleated by DAAM1 formin and stabilized by the actin crosslinking protein filamin A. The asters are connected with each other by myosin II, so that the entire system forms a contractile network responsible for the maintenance of the cell shape. (2) Observations of the assembly of myosin-II filament arrays by structured illumination microscopy (SIM) revealed myosin-II “stacks” formed by alignment in register of the myosin-II bipolar filaments associated with actin fibers. In the cells spread over the planar substrate, the numerous myosin stacks apparently form the links between neighboring actin filament bundles (stress-fibers or arcs), maintaining the organization of the actin cytoskeleton. (3) Globally, upon spreading on planar substrate s, cells develop chiral arrays of actin filament bundles. In fibroblasts confined to the circular adhesive islands, a radially symmetrical system of actin bundles, consisting of alpha-actinin-enriched radial fibers (RFs) and myosin-IIA-enriched transverse fibers (TFs), evolved spontaneously into the chiral system as a result of the unidirectional tilting of all RFs accompanied by a tangential shift in the retrograde movement of TFs. The handedness of the chiral pattern is regulated by alpha-actinin-1. Experimental observations together with computational modeling, demonstrated how the interactions between RFs nucleated by formins and contractile TFs could result in the transition of the actin pattern from radial to chiral, left-right asymmetric organization. Thus, actin cytoskeleton self-organization provides built-in machinery that potentially allows cells to develop left-right asymmetry. Such actin-based mechanism could underlie the development of left-right asymmetry in tissues and embryos. Related Links:
CGPW01 14th July 2015
16:00 to 17:00
Group Discussion
CGPW01 15th July 2015
09:00 to 10:15
Leah Edelstein-Keshet Models of cell polarization and motility
CGPW01 15th July 2015
10:45 to 12:00
Raymond Goldstein How a Volvox embryo turns itself inside out
During the growth of daughter colonies of the multicellular alga Volvox the spherical embryos must turn themselves inside out to complete their development. This process of 'inversion' has many features in common with gastrulation, the process by which an initially convex spherical shell of animal cells develops an invagination, leading to the formation of a gastric system. In both cases it is understood that cell shape changes play a major role in guiding the process, but quantification of the dynamics, and formulation of a mathematical description of the process, have been lacking. In this talk I will describe advances my group has made recently on both fronts. Using the technique of SPIM (selective plane illumination microscopy) we have obtained the first real-time three-dimensional time-lapse movies of inversion in Volvox, using several species displaying distinct morphological events. The beginnings of an elastic theory of these processes will also be described.
CGPW01 15th July 2015
13:30 to 14:45
Reinhard Windoffer The dynamic cytoskeleton
CGPW01 15th July 2015
15:15 to 16:30
Rudolf Leube Adhesions in epithelial cell migration
Collective cell migration is characteristic for epithelial cells requiring not only reversible attachment to the extracellular matrix but also continued cell-to-cell cohesion of the entire epithelial sheet. The different types of adhesive functions have been linked to morphologically and functionally distinct multimolecular complexes, which physically couple to the cytoskeleton and act as signaling centers. We will first describe the different types of adhesion sites that are characteristically encountered in epithelial tissues and present selected examples of human diseases linked to perturbation of these sites. Emphasis will be on the plasticity of the different junction types and their cross-talk with each other and other cellular elements. Finally, questions regarding modulation and function of the different adhesion modes will be discussed in the context of epithelial cell migration.
CGPW01 15th July 2015
16:30 to 17:00
Group Discussion
CGPW01 16th July 2015
09:00 to 10:15
Luigi Preziosi Multiscale Modelling of Cell-ECM interaction
Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels. In the talk, we will describe several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells. An energetic approach is used in order to obtain a necessary condition for which cells enter cylindrical structures. The nucleus of the cell is treated either (i) as an elastic membrane surrounding a liquid droplet or (ii) as an incompressible elastic material with Neo-Hookean constitutive equation. The results obtained highlight the importance of the interplay between mechanical deformability of the nucleus and the capability of the cell to establish adhesive bonds.
CGPW01 16th July 2015
10:45 to 12:00
Yoichiro Mori Osmosis, Electrophysiology and Cell Movement
Water movement in the biological tissue is controlled primarily by osmosis, and the primary osmolytes are ions (Na, K, Cl etc). It is then natural to think that electrophysiology is in some way related to cell movement. This indeed seems to be the case; there is mounting evidence that ion channels and aquaporins play an important role in cell movement. In this talk, we will first review some classical facts about electrophysiology, focusing on its role in cell volume control. We will also discuss the classical subject of fluid secretion/absorption in epithelial systems, and compare this with recent work on a mode of cell movement that seems to be predominantly osmotic. We will then present a mathematical framework that couples electrophysiology, osmosis and cell mechanics in a natural way that allows for the study of this interplay. We will show preliminary 2D computational results of a deforming model cell moving using osmotic forces.
CGPW01 16th July 2015
12:00 to 12:30
Group Discussion
CGPW01 16th July 2015
13:30 to 14:45
Rudolf Merkel Mechanobiology of cells
CGPW01 16th July 2015
15:15 to 16:30
Anne Ridley Cell Motility and Signalling to the Cytoskeleton
Cells move in response to extracellular cues in their environment. Cell motility is driven by the cytoskeleton, principally actin filaments and microtubules. Rho family GTPases are intracellular signal transducers that coordinate cell motility through their effects on the cytoskeleton and cell adhesions. Most of the 20 human Rho GTPases cycle between a GTP-bound active form and a GDP-bound inactive form, although RhoH and Rnd proteins are constitutively GTP-bound. Rho GTPases are activated in response to a wide variety of extracellular cues. Rho GTPases are regulated by and activate a complex network of proteins, including protein kinases, which lead to changes in cytoskeletal dynamics and cell contractility. I will describe results of RNAi screens we have carried out of Rho GTPase network components, including new links between Rho family members and protein kinases.
CGPW01 16th July 2015
16:30 to 17:00
Group Discussion
CGPW01 17th July 2015
09:00 to 10:15
Robert Nürnberg Parametric finite element methods for two-phase flow and dynamic biomembranes
In this talk I will discuss recent advances in the numerical analysis of front-tracking methods for two moving interface problems. In the first part of the talk I will concentrate on a parametric finite element approximation of two-phase flow. Here two fluids evolve in a domain, separated by an interface. Stress balance conditions on the interface lead to surface tension terms involving curvature. We employ a variational approximation of curvature that originates from the numerical
approximation of geometric evolution equations, such as mean curvature flow. The arsising finite element approximation of two-phase flow can
be shown to be unconditionally stable.
In the second part of the talk, building on the concepts introduced in the first part, I will present a numerical method for the
approximation of dynamic biomembranes. Once again two phases of fluid are separated by an interface, but here the interface is endowed with
an elastic curvature energy. This models the properties of the lipid bilayer structure of the biomembrane's cell walls. Combining ideas on
the numerical approximation of Willmore flow, two-phase flow and  surface PDEs on an evolving manifold we are able to introduce a stable
parametric finite element method for the evolution of biomembranes.

Suggested review articles:
Deckelnick, K., Dziuk, G., and Elliott, C. M. (2005). Computation of geometric partial differential equations and mean curvature flow.
Acta Numer., 14, 139--232.
Seifert, U. (1997). Configurations of fluid membranes and vesicles.Adv. Phys., 46, 13--137.
CGPW01 17th July 2015
10:45 to 12:00
Alain Goriely A brief review of the mathematics and mechanics of biological membranes, plates, and shell
Many biological structures, such as cellular walls, epithelial sheet, pollen tubes, and seashells can be modelled as two-dimensional objects. That is, these structures have a transverse length scale much smaller than the other two typical length scales. In this general lecture, I will review the basic aspects of the mathematics and mechanics of surfaces. I will start by reviewing the differential geometry of surface, then consider classical models for lipid bilayers and their use in cellular biology. I will describe how to model bio-elastic membranes, plates, and shells and how to extend classical models to include active and growth processes. I will apply these ideas to microbial filaments, bleb formation, and to urchin and seashell growth.
CGPW01 17th July 2015
12:00 to 12:30
Group Discussion
CGPW01 17th July 2015
13:30 to 14:45
Ana-Sunčana Smith Membrane dynamics
CGPW01 17th July 2015
15:15 to 16:30
Michael Kozlov Mechanisms shaping endoplasmic reticulum
Membranes of intracellular organelles and transport intermediates acquire shapes with large curvatures and complex morphologies, and undergo persistent remodeling by fission and fusion. We suggest a unifying mechanistic framework for understanding how specialized peripheral membrane proteins control the intracellular membrane curvature and dynamics, and address the effects of several specific proteins. Our consideration is based on two major mechanisms by which proteins shape membranes: shallow insertion into the membrane matrix of amphipathic or hydrophobic protein domains, and membrane attachment to the strongly curved and rigid faces of hydrophilic protein scaffolds. We considering the scaffolding mechanism, by model computationally the shaping of endoplasmic reticulum (ER ) membranes by oligomers of reticulon and DP1/Yop1 family proteins. We demonstrate that membrane molding by these proteins into nearly half-cylindrical shapes underlies generation of the whole plethora of complex morphologies observed to date in ER of different cells, which include ER tubules, sheets, inter-tubular three-way junctions, inter-sheet helicoidal connections and sheet fenestrations.
CGPW01 17th July 2015
16:30 to 17:00
Group Discussion
CGPW01 20th July 2015
09:00 to 10:15
Philip K Maini Case studies in modelling pattern formation
The generation of spatial pattern formation is still a largely unresolved problem in biology. Here we will review some classical models for pattern formation, including the Turing reaction diffusion model, models for chemotaxis, in the context of biological applications.
CGPW01 20th July 2015
10:45 to 12:00
Analysis of stochastic multiscale systems: derivation of coarse-grained models, calculation of effective coefficients and data driven approaches.
CGPW01 20th July 2015
12:00 to 12:30
Group Discussion
CGPW01 20th July 2015
13:30 to 14:45
Erik Sahai Tumor cell migration
CGPW01 20th July 2015
15:15 to 16:30
Nienke Vrisekoop Intravital microscopy of the immune system
CGPW01 20th July 2015
16:30 to 17:00
Group Discussion
CGPW01 21st July 2015
09:00 to 10:15
Dagmar Iber From networks to functions - computational models of Organogenesis
CGPW01 21st July 2015
10:45 to 12:00
David Umulis Quantitative imaging and mathematical modeling reveals new mechanisms for BMP-mediated patterning of zebrafish blastula embryos
CGPW01 21st July 2015
12:00 to 12:30
Group Discussion
CGPW01 21st July 2015
13:30 to 14:45
Sebastian Aland Phase field models for multiphase flow with applications to cell motility
Co-authors: Wieland Marth (TU Dresden, Germany), Axel Voigt (TU Dresden, Germany) Many processes in biological cells can be described as multiphase flow systems. In this lecture I will introduce the diffuse interface model for such systems. One advantage is the simple coupling to additional physical effects. In particular, I will show how to account for species concentrations in the bulk phases and on the interface. The approach will be illustrated by numerical simulation of endocytosis and cell motility.
CGPW01 21st July 2015
15:15 to 16:30
Perihan Nalbant TBA
CGPW01 21st July 2015
16:30 to 17:00
Group Discussion
CGPW01 22nd July 2015
09:00 to 10:15
Charlie Elliott PDEs on evolving domains
Recently with Aphonse and Stinner we have presented an abstract framework for treating the theory of well- posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces. This theory is applicable to variational for- mulations of PDEs on evolving spatial domains including moving hyper- surfaces. We formulate an appropriate time derivative on evolving spaces called the material derivative and define a weak material derivative in analogy with the usual time derivative in fixed domain problems; our set- ting is abstract and not restricted to evolving domains or surfaces. Then we show well-posedness to a certain class of parabolic PDEs under some assumptions on the parabolic operator and the data. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled bulk-surface system and an equation with a dynamic boundary condition. In this talk we give some background to applications in cell biology. We describe how the theory may be used in the development and numerical analysis of evolving surface finite element methods and give some computational examples involving the coupling of surface evolution to processes on the surface. We indicate how this approach may work for PDEs on general evolving domains. We will discuss briefly surface finite elements for finding surfaces in the context of models for biomembranes. We will indicate how other approaches might be applicable.

Background material: K. P. Deckelnick, G. Dziuk and C. M. Elliott Computation of Geometric PDEs and Mean Curvature Flow Acta Numerica (2005) 139–232
G. Dziuk and C. M. Elliott Finite element methods for surface partial differential equations Acta Numerica (2013) 289–396

CGPW01 22nd July 2015
10:45 to 12:00
James Glazier Making Virtual-Tissue Modeling an Integral Tool in Biology
CGPW01 22nd July 2015
12:00 to 12:30
Group Discussion
CGPW01 22nd July 2015
13:30 to 14:45
Masayasu Mimura Colonial patterns formed by chemotactic bacteria E. coli
Over the past ten years, our understanding of how spatio-temporal patterns in far from equilibrium systems has been gradually deepened. Collaborative research of experimental and theoretical works have discovered the mechanism how complex patterns were generated in biological systems. It is emphasized that genetics does not always reveal the occurrence of such patterns and even simple systems may generate ordered as well as chaotic patterns in a self-organized way. As an example, Budrene and Berg observed that chemotactic bacteria of E. coli produce regulated as well as complex colonial patterns., depending on initial concentration of nutrients, In particular, flower-like patterns called “chevron pattern” is interesting ([1], [2]). Budrene and Berg concluded that such patterns are produced in a self-organized way. Motivated by their conclusion, we propose a macroscopic PDE model and Budrene and Berg understand the mechanism behind such colonial patterns ([3], [4], [5]).

Keywords: colonial pattern formation, chemotactic mobility, self-organization.

REFERENCES [1] Budrene E. O and Berg, H. C.: Complex patterns formed by motile cells of Escherichia coli., Nature 349 pp.630~633 (1991) [2] Budrene E. O and Berg, H. C.: Dynamics of formation of symmetrical patterns by chemotactic bacteria, Nature 376 pp. 49~53 (1995 [3] Aotani A., Mimura M. and Mollee T.: A model-aided understanding of spot pattern formation in chemotactic E. coli colonies, Japan J. Industrial and Applied Mathematics, 27, 5-22 (2010) [4] Celinski, R., Hilhorst D., Karch G. and Mimura M.: Mathematical properties of solutions to the model of formation of chemotactic E. coli. colonies, manuscript [5] Aotani A. and Mimura M.: Chevron patterns in chemotactic E. coli. colonies, in preparation
CGPW01 22nd July 2015
15:15 to 15:45
Group Discussion
CGPW01 23rd July 2015
09:00 to 10:15
Mark Chaplain Multiscale modelling of cancer growth and treatment
CGPW01 23rd July 2015
10:45 to 12:00
John King Multiphase modelling of cells and tissues
CGPW01 23rd July 2015
12:00 to 12:30
Group Discussion
CGPW01 23rd July 2015
13:30 to 14:45
Zeno von Guttenberg Cell Migration Assays
The movement of cells between different points induced by certain events, biological signals or environmental inputs is called cell migration. This process is essential for a large number of physiological processes like wound healing and immune response, but also for a variety of diseases. Investigating for instance the migration and invasion of tumor and stromal cells to understand the basic principles, gives valuable input for novel approaches in the diagnosis of cancer, the prognosis and the development of new drugs. Key features of migration assays are the easy application, the reproducibility and the significance of the results. An overview is given about different established in vitro assay types which can be used to evaluate cell migration. The assays are divided in methods for kinetic analysis and for endpoint measurements and also in 2D and 3D migration. Problems and limitations are discussed and the respective read out as well as the mathematical interpretation is presented.
CGPW01 23rd July 2015
15:15 to 16:30
Christoph Möhl Quantitative imaging of migrating cells in vitro and in living tissues
During the past 20 years, imaging of specific proteins in living biological systems has become one of the most powerful techniques to investigate processes of life on the micro scale. By optical imaging of genetically encoded fluorescent reporters, the localization and dynamics of functional proteins can directly be observed in artificial cell culture systems as well as in whole animals. For studying the process of cell migration specific parts of the cytoskeleton (e.g. actin bundles or substrate adhesion sites) can be recorded in time-lapse movies. However, due to technical limitations it is not feasible to observe multiple target structures simultaneously in one experiment. Thus, the interplay of multiple cellular components such as the contractile actin-myosin network and force-transducing adhesion sites is difficult to investigate. I will discuss opportunities and limitations of optical imaging for studying cell migration by examples from my work on single cell migration as well as collective cell migration during embryonic development. Amongst others, I will present methods how to quantify cellular dynamics with image processing methods and how to integrate heterogeneous data from multiple independent observations to one consistent picture.
CGPW01 23rd July 2015
16:30 to 17:00
Group Discussion
CGPW01 24th July 2015
09:00 to 10:15
Alf Gerisch Sensitivity analysis and quantification of uncertainty
In this lecture we will review methods for the local and global sensitivity analysis as well as a stochastic collocation approach for the quantification of uncertainty. These techniques can provide additional insight into given models as well as guide future research. However, they also come with their own computational challenges, which will be discussed. The methods are illustrated using some instructive examples from pattern formation.
CGPW01 24th July 2015
10:45 to 12:00
John Lowengrub Computational methods for tissue and tumor growth
CGPW01 24th July 2015
12:00 to 12:30
Group Discussion
CGPW01 24th July 2015
13:30 to 14:45
Leif Dehmelt Biomolecular interaction assays
CGPW01 24th July 2015
15:15 to 16:30
Dorit Merhof Image analysis for biomedical applications - methods and software solutions
In this talk, an insight into today’s image analysis needs of biological and medical research groups and core facilities is provided based on the results of a survey conducted within German BioImaging. Furthermore, a survey of methods for biomedical image processing is provided, as well as an overview of existing software solutions.
CGPW01 24th July 2015
16:30 to 17:00
Group Discussion
CGP 11th August 2015
11:00 to 12:00
Emergent Parabolic Scaling of Nano-Faceting Crystal Growth
Nano-faceting of material interfaces is a paradigmatic, non-equilibrium self-assembly process which arises in a wide variety of physical settings; for example, high-efficiency photo-electrochemical cells yielding solar-energy storage through hydrogen production, and enantiomer-specific heterogeneous catalysts with application to biology. The dynamics of slightly undercooled crystal-melt interfaces possessing strongly anisotropic and curvature-dependent surface energy and evolving under attachment-detachment limited kinetics finds expression through a certain singularly perturbed, hyperbolic-parabolic, geometric partial differential equation. Among its solutions, we discover a remarkable family of 1D convex- and concave- translating fronts whose fixed asymptotic angles deviate from the thermodynamically expected {\em Wulff} angles in direct proportion to the degree of undercooling: a non-equilibrium ({\em thermokinetic}) effect.

We also present a novel geometric matched-asymptotic analysis that demonstrates that the slow evolution of the large-scale features of 1D solutions $\mathcal{I}$ are captured by a Wulff-faceted interface $\mathcal{A}$ evolving under an intrinsic facet dynamics. This emergent dynamics possesses a Peclet length $L_\text{p}$ below which a spatio-temporal symmetry of parabolic type appears. We thereby theoretically predict, and numerically verify, that within the sub-Peclet regime the universal scaling law $\mathcal{L} \sim t^{1/2}$ governs the time $t$ evolution of the characteristic length $\mathcal{L}$ of the interface $\mathcal{I}$.

Related Article: Stephen J. Watson, "Emergent Parabolic Scaling of Nano-Faceting Crystal Growth", Proceedings of the Royal Society A, Vol. 471 (Issue 2174) DOI: 10.1098/rspa.2014.0560

CGP 13th August 2015
11:00 to 12:00
Models in Wound Healing: Scar Tissue and Contraction
This talk will explain results from models on scar tissue formation and fibroblast populated collagen lattice contraction. The first set of models focus on the biochemical remodeling of the wound environment. The extracellular matrix is treated as a continuum, the cells are modeled as discrete objects,and the interactions between the two are investigated to better understand scar tissue formation. In the second set of models, mechanical forces are the focus to better understand wound contraction. Both the cells and the collagen lattice are modeled as discrete structures in the fibroblast populated collagen lattice models.
CGP 18th August 2015
11:00 to 12:00
Subdiffusion, Lévy walks and nonlinear fractional PDE's
The talk will be concerned with the extension of the classical fractional PDE's for the nonlinear case involving interactions of Lévy walks and subdiffusive particles.
CGP 20th August 2015
11:00 to 12:00
Non-Markovian Reaction-Transport: Modelling Biological Invasions
A common key feature of many biological invasions is the existence of rest phases during which individuals reproduce. Since this process alternates with phases of movement it is necessary to make use of a general description where both processes are coupled, i.e., cannot occur separately. However, some recent studies propose reaction-diffusion equations that lead to behaviours that cannot be physically accepted. In this talk I will show the reasons why these equations cannot be used and will present mesoscopic models adequate for biological invasions modelling.
CGP 25th August 2015
11:00 to 12:00
Patterns in Polarisable Elastic Active Layers
I explore a class of macroscopic continuous models with feedback interactions inducing spontaneous vector or nematic polarisation and mechanical deformation of elastic active media. Linear stabilityanalysis predicts, depending on the sign of feedback interaction coefficients, either monotonic or oscillatory instability of the homogeneous isotropic state. In the former case, the emerging pattern undergoes a slow coarsening process but permanent polarity may emerge when the system is topologically constrained. Oscillatory instabilities arise in active systems on a finite wavelength, and lead to complex wave patterns. Transition to a deformed polarised state may be frustrated in constrained geometry but leads to boundary undulations in free-boundary settings.
CGP 26th August 2015
11:00 to 12:30
Theoretical model for persistent and oscillatory cell motility
Cell movement has essential functions in development, immunity and cancer. Various cell migration patterns have been reported, such as Brownian motion, intermittent and persistent random-walks, but no general rule has emerged so far. Here, we show on the basis of experimental data in vitro and in vivo that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns. Recent extensions of this model describe the oscillatory motion of dendritic cells, which compare very well with experiments. Actin Flows Mediate a Universal Coupling between Cell Speed and Cell Persistence Maiuri P, Rupprecht JF, Wieser S, Ruprecht V, Benichou O, Carpi N, Coppey M, De Beco S, Gov N, Heisenberg CP, Crespo CL, Lautenschlaeger F, Le Berre M, Lennon-Dumenil AM, Raab M, Thiam HR, Piel M, Sixt M, Voituriez R, Cell 161 , 374-386 (2015)
CGP 27th August 2015
11:00 to 12:00
Lonely in a group: Single and collective cell behaviour in 3D environments
CGP 1st September 2015
11:00 to 12:00
Existence and Stability of Spike Clusters for Reaction-Diffusion Systems
We study the existence and stability of spike clusters for biological reaction-diffusion systems with two small diffusion constants. In particular we consider a consumer chain model and the Gierer-Meinhardt system with a precursor gradient. In a spike cluster the spikes converge to the same limiting point. We will present results on the asymptotic behaviour of the spikes including their shapes, positions, and amplitudes. We will also compute the asymptotic behaviour of the eigenvalues. Such systems and their solutions play an important role in biological modelling to account for the bridging of lengthscales, e.g. between genetic, nuclear, intra cellular, cellular and tissue levels, or for the hierarchy of biological processes, e.g. first a large scale structure appears and then it induces patterns on a smaller scale. This is joint work with Juncheng Wei.
CGP 3rd September 2015
11:00 to 12:00
T Sekimura A model for selection of eyespots on butterfly wings
The development of eyespots on the wing surface in butterflies of the Family Nympalidae is one of the most studied examples of biological pattern formation. However, little is known about the mechanism that determines global pattern elements such as the number and precise locations of eyespots on the entire wing. Eyespots develop around signaling centers, called foci of a group of focal cells, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the entire wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal veins, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points.
CGP 8th September 2015
11:00 to 12:30
Localized pulse solutions in FitzHugh-Nagumo equations
Particle-like structures are commonly observed in physical, chemical and biological systems. Depending on the system parameters and initial conditions, localized dissipative structures may stay at rest or propagate with a dynamically stabilized velocity. In this talk we aim at some variational methods for studying pulse solutions to FitzHugh-Nagumo equations.
CGP 10th September 2015
11:00 to 12:30
Minimising a relaxed Willmore functional for graphs subject to Dirichlet boundary conditions
For a bounded smooth domain $\Omega$ in the plane we consider the minimisation of the Willmore functional for graphs subject to Dirichlet boundary conditions. In a first step we show that sequences of functions with bounded Willmore energy satisfy uniform area and diameter bounds yielding compactness in $L^1(\Omega)$. We therefore introduce the $L^1$--lower semicontinuous relaxation and prove that it coincides with the Willmore functional on the subset of $H^2(\Omega)$ satisfying the given Dirichlet boundary conditions. Furthermore, we derive properties of functions having finite relaxed Willmore energy with special emphasis on the attainment of the boundary conditions. Finally we show that the relaxed Willmore functional has a minimum in $L^{\infty}(\Omega) \cap BV(\Omega)$. This is joint work with Hans--Christoph Grunau (Magdeburg) and Matthias Röger (Dortmund).
CGPW02 14th September 2015
10:00 to 11:00
Anne Ridley Cell motility and signalling to the cytoskeleton
CGPW02 14th September 2015
11:30 to 12:30
Rudolf Leube Epithelial intermediate filament organisation: Modes of regulation in vitro and in vivo
The keratin intermediate filament cytoskeleton is a hallmark feature of epithelial cells. Molecular diversity is the basis of its finely tuned contribution to epithelial mechanics and function. Time-lapse analysis has revealed an unexpected degree of continuous re-structuring of the keratin scaffold in cultured epithelial cells. Multiple factors including other cytoskeletal filaments, cell adhesion sites and growth factors regulate keratin dynamics in vitro. The mechanisms governing the cell type-specific organisation of the keratin network in living organisms is much less understood. Yet, the polarized distribution of intermediate filaments in simple, one-layered epithelia is conserved from the nematode Caenorhabditis elegans to mammals. The use of recently established fluorescent reporter strains now allows monitoring and elucidating intermediate filament morphogenesis in vital tissues and organisms.
CGPW02 14th September 2015
13:30 to 14:15
Christian Schmeiser The Filament Based Lamellipodium Model: a continuum model derived from actin filament dynamics
Co-authors: Angelika Manhart (Univ. of Vienna), Dietmar Oelz (New York Univ.), Nikolaos Sfakianakis (Univ. Mainz), J. Vic Small (Inst. f. Molecular Biotechn. Austria)

The lamellipodium is a flat cell protrusion functioning as a motility organelle for cells on flat substrates. It is a very dynamic structure mainly consisting of a network of filaments of polymerized actin. The Filament Based Lamellipodium Model is a two-dimensional, two-phase, anisotropic continuum model for the dynamics of this network, which has been developed over the past 8 years. It has been derived from a microscopic description based on the dynamics and interaction of individual filaments. Some aspects of the derivation of the model, of its analysis, and of its numerical solution will be presented, together with some recent simulation results.

CGPW02 14th September 2015
14:15 to 15:00
Andrew Goryachev The cell cortex is an excitable medium
Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs assembly of actomyosin in the equatorial cortex. We show that shortly after anaphase onset oocytes and embryonic cells of frogs and echinoderms exhibit cortical waves of Rho activity and F-actin polymerization. The waves are modulated by cyclin-dependent kinase 1 (Cdk1) activity and require the Rho GEF (guanine nucleotide exchange factor), Ect2. Surprisingly, during wave propagation, while Rho activity elicits F-actin assembly, F-actin subsequently inactivates Rho. Experimental and modeling results show that waves represent excitable dynamics of a reaction diffusion system with Rho as the activator and F-actin the inhibitor. We propose that cortical excitability explains fundamental features of cytokinesis including its cell cycle regulation.
CGPW02 14th September 2015
15:30 to 16:00
Discussion: what do we want to learn?
CGPW02 14th September 2015
16:00 to 17:00
C Elliott Solving PDEs in domains with complex evolving morphology: Rothschild Visiting Fellow Lecture
Many physical models give rise to the need to solve partial differential equations in time dependent regions. The complex morphology of biological membranes and cells coupled with biophysical mathematical models present significant computational challenges as evidenced within the Newton Institute programme "Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation". In this talk we discuss the mathematical issues associated with the formulation of PDEs in time dependent domains in both flat and curved space. Here we are thinking of problems posed on time dependent d-dimensional hypersurfaces Gamma(t) in R^{d+1}. The surface Gamma(t) may be the boundary of the bounded open bulk region Omega(t). In this setting we may also view Omega(t) as (d+1)-dimensional sub-manifold in R^{d+2}. Using this observation we may develop a discretisation theory applicable to both surface and bulk equations. We will present an abstract framework for treating the theory of well- posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces using generalised Bochner spaces. This theory is applicable to variational formulations of PDEs on evolving spatial domains including moving hyper-surfaces. We formulate an appropriate time derivative on evolving spaces called the material derivative and define a weak material derivative in analogy with the usual time derivative in fixed domain problems; our setting is abstract and not restricted to evolving domains or surfaces. Then we show well-posedness to a certain class of parabolic PDEs under some assumptions on the parabolic operator and the data. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled bulk-surface system and an equation with a dynamic boundary condition. We give some background to applications in cell biology. We describe how the theory may be used in the development and numerical analysis of evolving surface finite element spaces which unifies the discrtetisation methodology for evolving surface and bulk equations. In order to have good discretisation one needs good meshes. We will indicate how geometric PDEs may be used to compute high quality meshes. We give some computational examples from cell biology involving the coupling of surface evolution to processes on the surface.
CGPW02 15th September 2015
09:00 to 10:00
Denis Wirtz Cancer Cell Migration in 3D
Two-dimensional (2D) in vitro culture systems have for a number of years provided a controlled and versatile environment for mechanistic studies of cell adhesion, polarization, and migration, three interrelated cell functions critical to cancer metastasis.  However, the organization and functions of focal adhesion proteins, protrusion machinery, and microtubule-based polarization in cells embedded in physiologically more relevant 3D extracellular matrices is qualitatively different from their organization and functions on conventional 2D planar substrates. This talk will describe the implications of the dependence of cell migratory patterns, protrusion generation, force generation, and cell mechanics on 3D settings.
CGPW02 15th September 2015
10:00 to 11:00
Robert Kay How cells form cups
Many cells can take in relatively large solid objects or droplets of medium by forming cup-shaped structures from their plasma membrane. These projections extend, close, and after membrane fusion produce an intracellular vesicle in which the contents can be digested and useful molecules extracted. Cups are extended from the plasma membrane by a ring of actin polymerization which can be several microns in diameter. In the uptake of solid particles – phagocytosis – the particle itself is thought to trigger uptake and guide formation of the cup that engulfs it. However, in the case of fluid uptake, no such template is available, and the questions arises of how can a cell organize actin polymerisation into a ring? Dictyostelium amoebae are adept at both phagocytosis and macropinocytosis, and I will describe how our recent work leads to a hypothesis of actin ring formation.

CGPW02 15th September 2015
11:30 to 12:30
Stephanie Portet Modelling intermediate filaments
Intermediate filaments are one of the components of cytoskeletal networks. Intermediate filaments play a crucial role in the cell mechanics. Understanding their assembly dynamics, organization in networks and resulting mechanical properties is essential to elucidate their functions in cells. A combination of mathematical modelling and experimental data is used to investigate the organization of the intermediate filament networks. What contributes to their organization? What process or combination of processes does the organization emerge from? What process dominates?
CGPW02 15th September 2015
13:30 to 14:15
Thomas Woolley Cellular blebs: pressure-driven, axisymmetric, membrane protrusions
Human muscle undergoes an age-related loss in mass and function. Preservation of muscle mass depends, in part, on stem cells, which navigate along muscle fibres in order to repair damage. Critically, these stem cells have been observed to undergo a new type of motion that uses cell protrusions known as “blebs”, which protrude from the cell and permit it to squeeze in between surrounding material.

By solving the diffusion equation in polar coordinates we have mathematically investigated this blebbing phenomenon with a particular focus on characterizing the effect of age on cell migration. Our results have then been fitted to experimental data allowing us demonstrate that young cells move in a random ‘‘memoryless’’ manner, whereas old cells demonstrate highly directed motion, which would inhibit the chances of a cell finding and repairing damaged tissue.

Further, we have constructed a mechanical model for the problem of pressure-driven blebs based on force and moment balances of an axisymmetric shell. Through investigating multiple extensions of this model we find numerous results concerning size, shape and limiting factors of blebs. Finally, leading us to consider much simpler equations which allow us to connect motion to mechanical properties of the cell, thus, coming full circle in our research.
CGPW02 15th September 2015
14:15 to 15:00
José Manuel García Aznar Modelling 3D cell motility in mechano-chemo-biology: from microfluidics to numerical simulation
Co-authors: Moreno-Arotzena O (Universidad de Zaragoza), Ribeiro F (IST Lisbon), Borau C (Universidad de Zaragoza)

Cell motility is essential for many morphogenetic and regenerative processes, also contributing to the development of numerous diseases, including cancer. For 2D, cell movement starts with protrusion of the cell membrane followed by the formation of new adhesions at the cell front that link the actin cytoskeleton to the extracellular matrix, generation of traction forces that move the cell forwards and disassembly of adhesions at the cell rear. Although valuable knowledge has been accumulated through analysis of various 2D models, some of these insights are not directly applicable to migration in 3D. In any case, all these processes are regulated by environmental signals from the surrounding microenvironment that allow cells to guide and regulate their directional movement. Unraveling the intrinsic mechanisms that cells use to define their migration is crucial for advancing in the development of new technologies in regenerative medicine and treatment of cancer. Due to the complexity of all these mechanisms, the combination of in-vitro models (through microfluidics-based experiments) and computational simulations provide deeper insight and quantitative predictions of the mechano-chemical interplay between cells and extracellular matrix during migration With this objective in mind, we have developed microfluidic-based studies of individual 3D fibroblast movement in biomimetic microenvironments provided by the matrix and the biochemical factors that are moving in the medium. In particular, we have confined two physiologically relevant hydrogels (collagen and fibrin) in combination with two growth factors (PDGF-BB and TGF-β1). Meanwhile, we are developing novel numerical approaches that combine discrete and continuous numerical approaches in order to simulate this 3D cell migration. So, in this work, I will show recent progress that we have made in the development of different integrative numerical strategies for advancing in the simulation of cell movement in 3D
CGPW02 15th September 2015
15:30 to 16:15
John Mackenzie A Computational Model for Single Cell Migration and Chemotaxis: Coupling Bulk and Membrane Bound Processes
Co-authors: Michael Nolan (University of Strathclyde), Grant McDonald (University of Strathclyde), Matt Neilson (Beatson Institute for Cancer Research), Robert Insall (Beatson Institute for Cancer Research)

In this talk I will present details about a moving mesh finite element method for the approximate solution of partial differential equations on an evolving bulk domain in two dimensions, coupled to the solution of partial differential equations on the evolving domain boundary. Problems of this type occur frequently in the modelling of eukaryotic cell migration and chemotaxis - for these applications the bulk domain is either the intracellular or extracellular region and the domain boundary is the cell membrane. Fundamental to the success of the method is the robust generation of bulk and surface meshes for the evolving domains. For this purpose we use a moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known solutions which indicate second-order spatial and temporal accuracy. The method is then applied to a model of the two-way interaction of a migrating cell with an external chemotactic field.
CGPW02 15th September 2015
16:15 to 17:00
Michael Beil Cell mechanics as a target to regulate extravasation of neutrophils
CGPW02 16th September 2015
09:00 to 10:00
Carl-Philipp Heisenberg TBA
CGPW02 16th September 2015
10:00 to 11:00
Benjie Ovryn Modeling and tracking glycan diffusion near integrin adhesions using biorthogonal click-chemistry and interference microscopy
The dynamics of integrin adhesion to the extracellular matrix (ECM) is critical for cell motility and growth, yet metastatic cells are capable of anchorage-independent survival with loss of adhesion from the primary tumor and subsequent adhesion in the microenvironment of the metastatic niche. Unfortunately, we do not yet have a clear understanding of the detailed mechanisms that govern the nucleation, clustering and adhesion of integrins to the ECM in the presence of the myriad of cell-surface glycoproteins that extend into the extracellular space. In order to explore how interactions between integrins and glycans alter clustering and adhesion, we have adopted a three-pronged approach that includes: (1) modeling the energetic landscape that governs membrane bending and integrin adhesion; (2) tracking bioorthogonally tagged cell-surface glycans with single-molecule sensitivity and (3) measuring membrane topography using phase-shifted laser feedback interference microscopy.
CGPW02 16th September 2015
11:30 to 12:30
Kees Weijer Light sheet microscopy reveals the cellular mechanisms driving primitive streak formation
Co-authors: Emil Rozbicki (University of Dundee), Manli Chuai (University of Dundee), Antti Karjalainen (University of Dundee), Micheal MacDonald (University of Dundee)

Gastrulation involves embryo wide tissue reorganizations and deformations driven by coordinated cell shape changes and rearrangements that cannot be imaged using normal microscopic methods. To be able to image the detailed cell behaviors of >200.000 cells we have implemented a scanned light sheet microscope dedicated to imaging large flat samples. This microscope includes dynamics surface tracking method that allows us to keep the embryo in focus of the light sheet during the scanning process. Using this LSM we show that the large scale tissue deformations resulting in the formation the primitive streak in the chick embryo are driven by anisotropic pulling forces generated by cell shape changes and local rearrangements of mesendoderm cells. Cell rearrangements are mediated by sequential, directional contraction of temporary aligned apical junctions in asymmetrically shaped neighboring cells, a process driven by apical acto-myosin II cables that assemble in a Myosin I depen dent manner. The role of Myosin I in the coordination of contraction of junctions in neighboring cells suggests a key role for tension sensing in the assembly and activation of Myosin II cables [1]. We have now implemented an improved method able to track an area of interest, allowing the imaging of cell behaviors at high magnification in tissues undergoing active large scale flows and deformations. This allows study of the detailed cell behaviors during the ingression of mesoderm cells into the primitive streak, a key process in the embryonic development of higher organisms including humans. References [1.] Rozbicki, E., et al., Myosin-II-mediated cell shape changes and cell intercalation contribute to primitive streak formation. Nat Cell Biol, 2015. 17(4): p. 397-408.

CGPW02 16th September 2015
13:30 to 14:15
Edward Green Mathematical models for cell-extracellular matrix interactions in tissue development
Mechanical interactions between cells and the fibrous extracellular matrix (ECM) in which they reside play a key role in tissue development. Mechanical cues from the environment (such as stress, strain and fibre orientation) regulate a range of cell behaviours, including proliferation, differentiation and motility. In turn, the ECM structure is affected by cells exerting forces on the matrix which result in deformation and fibre realignment. We present a mathematical model to investigate this mechanical feedback between cells and the ECM. We consider a three-phase mixture of collagen, culture medium and cells, and formulate a system of partial differential equations which represents conservation of mass and momentum for each phase. This modelling framework takes into account the anisotropic mechanical properties of the collagen gel arising from its fibrous microstructure. We also propose a cell-collagen interaction force which depends upon fibre orientation and collagen density. We use a combination of numerical and analytical techniques to study the influence of cell-ECM interactions on pattern formation in tissues. Our results illustrate the wide range of structures which may be formed, and how those that emerge depend upon the importance of cell-ECM interactions.
CGPW02 16th September 2015
14:15 to 15:00
Self-organization of adipose tissue
One of the key functions of adipose tissue is to store energy for the needs of the organism. Dysfunction of adipose tissue results in conditions like obesity which affect an increasing number of people worldwide. In 2007, it was estimated that 50% of women and 65% of men in UK were overweight or obese. Yet, very few studies of how adipose tissue organizes during its development are available. The fat storing cells or adipocytes are organized in lobular structures separated by collagen fiber septa. In this work, we use an individual-based model to investigate scenarios for the formation of these lobules. We find that they could result from the combination of volume exclusion constraints between the adipocytes and confinement by the elasticity of the collagen fibers. In particular, the model shows that vasculature does not seem to notably influence the outcome of this morphogenesis process. This study suggests that the role of vaculature in adipogenesis could be more complex than originally thought.
CGPW02 16th September 2015
15:30 to 16:15
Bakhtier Vasiev Modelling chemotactic motion of cells in biological tissues
Developmental processes in biology are underlined by proliferation, differentiation and migration of cells. The latter two are interlinked since cellular differentiation is governed by the dynamics of morphogens which, in turn, is affected by the movement of cells. Mutual effects of morphogenetic and cell movement patterns are enhanced when the movement is due to chemotactic response of cells to the morphogens. In this presentation I introduce mathematical models to analyse how this interplay results into formation of propagating wave solution in a concentration field of a morphogen and associated steady movement of cells in tissue. It is found that a single cell or a group of cells of certain cell type surrounded by cells of another type can push itself to move, provided that it produces a chemical which acts as a chemorepellent to its constituent cells. Also, the group of cells can be pulled to move if it is attracted by a morphogen produced by the surrounding cells in a ti ssue. Even when the group is formed by cells which are not chemotacticaly active, it can move when surrounding cells are attracted chemotactically by the morphogen produced outside the moving group or repelled by the morphogen produced inside the group. In all cases the motion is possible if the chemotactic response is stronger than a certain threshold defined by the kinetics of the morphogen. The model is also extended to consider proliferation and differentiation of cells forming the moving group.
CGPW02 16th September 2015
16:15 to 17:00
Behruz Bozorg Mechanical signals and morphogenesis in plants
Plants undergo large deformations during organ initiation and growth. Recent evidence is revealing the role of mechanical cues in these morphogenic events. Here we summarise our efforts to include properties such as varying elasticity, plasticity and mechanical anisotropy in time and space for modelling the plant tissue. Due to the key role of plant epidermis in morphogenesis, the plant tissue can be modelled as a pressure vessel. We modified the well known Saint-Venant's strain energy model to represent anisotropic material. In our model the tuneable material anisotropy resembles fiber deposition in primary plant walls. In the meristem periphery circumferential cellulose fiber organisation is the main controller of longitudinal growth. In our model this can be achieved by applying a feedback from maximal stress direction to the fiber orientation. By considering the degree of material anisotropy and anisotropy direction as additional variables in a linear material model u nder plane stress condition, we could show that stress feedback model is in fact an energy minimization process. Though this finding is not sufficient to describe the underlying mechanism of potential stress feedback, it could be considered as an evolutionary motivation. We employed strain signal for regulating the differential plastic deformation. We showed that the behaviour of such model is mesh independent and in case of being used together with stress feedback model for anisotropic tissue can result in overall deformations favourable for development of plant-like shapes. Ignoring the internal structure in tissue pressure models is not realistic in various cases. Some patterning processes such as vein formation in meristem need to be investigated throughout the three dimensional structure of the tissue. We have also extended our model to study the capability of mechanical signals regulating the cell polarity which are crucial to Auxin patterning processes including the internal tissue structure.
CGPW02 17th September 2015
09:00 to 10:00
Sean Gregory Megason Mechanical feedback via pressure regulates organ size
Co-authors: Kishore Mosaliganti (), Ian Swinburne (), Tom Hiscock (), L. Mahadevan (Department of Physics and School of Engineering and Applied Science, Harvard University)

Animals develop tissues of precise size, shape, and symmetry despite noise in the underlying molecular and cellular processes. How tissue and organ-level feedback regulates this noise is largely unknown. The Megason lab combines quantitative imaging, physical theory and perturbations in zebrafish to study size control of the developing inner ear and neural tube.

In the inner ear, we find that transepithelial fluid flow creates hydrostatic pressure in the lumen leading to stress in the otic epithelium and expansion of the otic vesicle. Pressure, in turn, inhibits endolymph transport into the lumen. This negative feedback loop between pressure and fluid flux allows the otic vesicle to change growth rate in order to regulate natural or experimentally induced size variation. Furthermore, the shape of the inner ear is modulated by spatial-temporal patterning of actomyosin contractility allowing a common lumenal pressure to drive varying local epithelial strain rates. This work uncovers how molecular driven mechanisms such as osmotic force generation and actomyosin tension can regulate tissue level morphogenesis via hydraulic feedback to ensure robust control of organ size.

We also find evidence for pressure-based feedback in the neural tube but at a very different spatial scale. Here, pressure forces created by single cells in mitosis influence the fate of adjacent cells in order to properly balance proliferation and differentiation rates to generate the right number of neurons despite variation in the process.
CGPW02 17th September 2015
10:00 to 11:00
Paul Kulesa Moving Cells Throughout the Embryo: A Story from the Neural Crest
Co-authors: Rebecca McLennan (Stowers Institute), Linus Schumacher (University of Oxford), Jason Morrison (Stowers Institute), Ruth Baker (University of Oxford), David Kay (University of Oxford), Philip Maini (University of Oxford)
The neural crest are an excellent model to study in vivo mechanisms of embryonic cell migration since cells display directed migration in discrete streams that travel long distances to precise targets. In the vertebrate head, cranial neural crest cells form bone, cartilage, neurons and glia making their migration absolutely critical to craniofacial patterning. How neural crest cells move as a coordinated population is not well understood. We have discovered that coordinated cranial neural crest migration includes lead cells with distinct cell dynamics, cell morphologies and molecular profiles consistent with maintaining directed migration. Our single cell profiing of leaders has revealed a unique molecular signature of genes highly expressed and consistent within a trailblazer subpopulation narrowly confined to the migratory front. We hypothesize that trailblazer genes serve a critical functional role for neural crest cells to establish directed migration and separate instruc tional signals are communicated to trailer cells to follow. We will discuss our modeling and experimental results.
CGPW02 17th September 2015
11:30 to 12:30
Kishore Mosaliganti Lumenogenesis: Understanding fluid flow into a closed cavity
Co-authors: Ian Swinburne (Harvard Medical School), Sean Megason (Harvard Medical School)

Most internal organs including the eyes, lung, gut, kidney, bladder, brain, and vascular system, all begin as epithelialized cysts or tubes with a fluid-filled lumen. Developmental growth of these tissues is regulated by the transepithelial fluid transport. In the zebrafish inner ear, recent work in the Megason Lab showed that transepithelial flow creates hydrostatic pressure in the lumen, which in turn, inhibits fluid transport rates to control overall vesicle growth rate. As a first step to linking pressure forces to transport mechanisms, the origin, path, and physical mechanism underlying fluid movement needs to be identified. Quantitative imaging shows that extracellular, but not intracellular, fluid is transported from basal to apical ends of the epithelium. Dye-tracing experiments revealed localization patterns of dye in paracellular spaces indicative of the movement of fluid. To verify if fluid flow is coupled with dye patterns, we developed a mathematical model that s howed that advective dye movement is sufficient to explain experimental outcomes. In general, the transport of salts and fluid across an epithelium occurs via electrogenic pumps/transporters and aquaporins on cell membranes, or paracellularly through cell-cell junctions. However, in "leaky" epithelia, it is not clear how such gradients can be sustained to drive rapid transport of fluid for growth. Previous work in the otic vesicle identified the activity of Na-K-ATPase in setting up a spontaneous electrical potential to drive the selective movement of water and ions. However, we show that Na-K channels are uniformly expressed throughout the cell membrane and their expression levels drop before the period of rapid growth. Using state-of-the-art light-sheet microscopy, we show new visualizations of pulsatile fluid movement through paracellular spaces. Thus, our current data suggests that other, as yet unknown, intermediate cellular mechanisms could facilitate the unidirectional movement of fluid.
CGPW02 17th September 2015
13:30 to 14:15
Sharon Lubkin What’s lumen got to do with it? Mechanics and transport in lung morphogenesis
Mammalian lung morphology is well optimized for efficient bulk transport of gases, yet most lung morphogenesis occurs prenatally, when the lung is filled with liquid - and at birth it is immediately ready to function when filled with gas. Lung morphogenesis is regulated by numerous mechanical inputs including fluid secretion, fetal breathing movements, and peristalsis. We generally understand which of these broad mechanisms apply, and whether they increase or decrease overall size and/or branching. However, we do not have a clear understanding of the intermediate mechanisms actuating the morphogenetic control. We have studied this aspect of lung morphogenesis from several angles using mathematical/mechanical/transport models tailored to specific questions. How does lumen pressure interact with different locations and tissues in the lung? Is static pressure equivalent to dynamic pressure? Of the many plausible cellular mechanisms of mechanosensing in the prenatal lung, which a re compatible with the actual mechanical situation? We will present our models and results which suggest that some hypothesized intermediate mechanisms are not as plausible as they at first seem.
CGPW02 17th September 2015
14:15 to 15:00
Axel Voigt A mechanical basis for axes alignment in early embryogenesis - cortical flow and cytoplasmic streaming
Co-authors: Stephan Grill (BIOTEC - TU Dresden), Peter Gross (BIOTEC - TU Dresden), Michael Nestler (TU Dresden)

Axis alignment in early embryogenesis refers to the alignment of the principal body axis with the long axis of the embryonic eggshell. This process is important for ensuring proper cell and tissue arrangement in morphogenesis. In C. elegans zygotes, the process of aligning the anteroposterior axis of cell polarity with the long axis of the embryo eggshell is referred to as posteriorization. It arises during cell polarization and appears to be driven through cortical and cytosolic flows. Here we discuss the underlying mechanical basis of posteriorization and axis convergence by combined experimental and numerical investigations. We consider the two-way interplay between actively driven surface flow in the actomyosin cortical layer and cytoplasmic streaming, and study the redistribution of the flow organizer (the male pronucleus) through cytoplasmic streaming for axis convergence. The underlying mathematical model consideres a bulk/surface coupling which is realized using a dif fuse domain/diffuse interface approach, which will be discussed in detail together with the strong interplay between local curvature, surface and bulk flow.
CGPW02 17th September 2015
15:30 to 16:15
Bjorn Stinner Surface finite element methods
Co-authors: Charles Elliott (University of Warwick), Paola Pozzi (University of Duisburg-Essen), Chandrasehkar Venkataraman (University of Sussex)

Complex phenomena such as moving cells may involve phenomena or processes on lower dimensional objects that separate compartments, phases, or other types of domains. Surface finite elements can provide a mean to approximate solutions to continuum models and, thus, after defining suitable objectives to compare with experimental data. In this context, we will report on new findings regarding the convergence analysis of schemes for simple coupled systems consisting of a geometric PDE for a curve and a diffusion equation on that curve. More sophistical systems of such a structure can be applied in cell biology where we exemplary look at the quantification of an approach to cell migration and, time permitting, focal adhesions and tethering of elastic membranes.

CGPW02 17th September 2015
16:15 to 17:00
Xiaoyu Luo Modelling Residual Stresses Modelling Residual Stresses in Heart and Arteries
This talk will start with an overview of the invariant-based continuum mechanics approach for anisotropic soft tissues that undergo large nonlinear deformation. I will then focus on the modelling of residual stress in such a setting. Residual stress is important in the mechanical behaviour of the living organs, and reflects the accumulated changes due to growth and remodelling over time. However, in many computational models, effects of residual stresses are overlooked. I will report how we consider the residual stress using the opening angle method with applications to left ventricle and aortic dissection. Results with and without the residual stress will be discussed. Finally, I will show that although it is commonly accepted that residual stress may be released in arteries from a single radial cut, this is not true in general. Indeed with two cuts or more, the maximum residual hoop stress could be as great as 35 times compared to that of the single cut. Further work is clearly required to investigate this and to link the continuum models to growth and modelling processes occurred at the cellular levels. Key words: residual stress, opening angle method, left ventricle model, aortic dissection.

CGPW02 18th September 2015
09:00 to 10:00
Ulrich Schwarz How cell forces shape tissue dynamics: from experiments to models
Co-authors: Carina Dunlop (University of Surrey), Christoph Koke (Heidelberg University), Takuma Kanesaki (Göttingen University), Jörg Grosshans (Göttingen University), Philipp Albert (Heidelberg University)

In this contribution we will use two different biological model systems to illustrate how experimental observations can be integrated in appropriate mathematical models that describe tissue dynamics as they emerge from the cytoskeletal forces generated by single cells. Our first example is the syncytium of Drosophila melanogaster, which is shared by up to 6.000 nuclei that before cellularization divide four times in a thin layer without forming cell walls. Using confocal microscopy, quantitative image processing, tracking of single nuclei and evaluation of an appropriate measure for order, we have shown that each division constitutes a significant disordering of the nuclear array that is restored within a few minutes by the syncytial cytoskeleton. Interestingly, between divisions actin caps act as spacers while microtubules impart some attractive interactions. We have implemented these cytoskeletal elements in an individual-based computer simulation that predict under which conditions a stable ordering process will occur. Our second example is the dynamics of cell monolayers on flat substrates, an important model for wound healing. We investigate this situation with a cellular Potts model extending our earlier work on single cells. While cell-cell adhesion together with actomyosin contractility ensures the cohesion of this system, cell-matrix adhesion together with actin-based protrusion makes the cell monolayer highly dynamic. We have implemented observation-based rules for cell mechanics, adhesion, divison and movement in a computationally very efficient simulation framework. Our model describes a large range of experimental data, including the dynamics and shapes of cell monolayers on micropatterned adhesive substrates.

CGPW02 18th September 2015
10:00 to 11:00
Jocelyn Etienne Rheology of actomyosin and emergent mechanical properties of cells
CGPW02 18th September 2015
11:30 to 12:30
Roeland Merks Multiscale cell-based modeling of mechanical cell-matrix feedback during collective cell behavior
Co-authors: Elisabeth G. Rens (CWI and Leiden University), René F.M. van Oers (CWI (present address: Oral Cell Biology, Academic Centre for Dentistry Amsterdam (ACTA), The Netherlands))

Apart from molecular signals, mechanical cell-cell communication is key to explaining collective cell behavior biological morphogenesis. Yet, most computational models of collective cell behavior focus on chemical signaling. Endothelial cell cultures on compliant substrates are a good model system of mechanical signaling during morphogenesis. Depending on the stiffness and other biophysical and chemical properties of the substrates, the endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Here we discuss a hybrid Cellular Potts and finite element computational model, in which a limited set of biologically plausible rules describing the mechanical cell-ECM interactions suffices for reproducing aspects of endothelial cell behavior at the single cell, pairwise and collective scale. The model includes the contractile forces that endothelial cells exert on the ECM, the resulting strains in the extracellular matrix, and the cellular resp onse to the strains. The simulations reproduce the behavior of individual endothelial cells, the interactions of endothelial cell pairs in compliant matrices, and network formation and sprouting from endothelial spheroids. We will conclude by showing how the mechanical interactions between cells and the extracellular matrix amplify the dynamic response of tissue organization to external strain. This response offers a potential route by which large scale strains in growing embryos can control the cellular structure of tissues.

CGPW02 18th September 2015
13:30 to 14:15
Chandrasekhar Venkataraman Image driven modelling of cell motility
Modern molecular biology, microscopy and imaging techniques allow the acquisition of large amounts of high resolution images of migrating cells. In this talk, I will present some initial steps towards using such imaging data in the development of mathematical models of cell migration. Time permitting, we will focus on two examples, a model for monopolar and bipolar growth of the fission yeast S. Pombe and a phase field approach to whole cell tracking. The first involves the use of qualitative features observed in the data to refine the modelling while the second illustrates some first steps towards model quantification using imaging data.

CGPW02 18th September 2015
14:15 to 15:00
Naomi Nakayama Self-calibration of structural engineering in plant shoots
The shapes of living organisms are determined not only by their physiological function, but also by the engineering stability of their body. Recently mechanical parameters of tissues are emerging as important regulators of multicellular development; both intrinsic and external mechanical stimuli can impact cell division, growth, and differentiation. This is particularly the case in plants, which can adjust their morphology and anatomy according to the mechanical demands imposed upon them. How plants sense and respond to mechanical stimuli to sustain their structural stability is an exciting question that remains largely unexplored. My group aims to comprehend mechanically induced developmental plasticity in the model plant Arabidopsis, through a highly integrative programme encompassing biochemistry and systems biology to computer simulation and material science analyses. Self-stabilisation of plant shoot engineering is mediated by the accumulation dynamics of phytohormone au xin, a major morphogen in plants that is sensitive to mechanical strain and stress. We are currently developing a microfluidics platform to characterise mechano-sensing and immediate responses at the cellular level. Since engineering stability of plants is also crucial to agriculture, we are also exploring improvement of cereal grain production via mechanical stimulation. Specifically, we are investigating the molecular and engineering mechanisms behind a longstanding agricultural practice in Japan called mugi-fumi, which reduces structural failure of wheat and barley plants by simple mechanical treatments.

CGPW02 18th September 2015
15:30 to 16:15
John King Cellular patterning in plant roots
Co-authors: Anthony Bishopp (University of Nottingham), Nathan Mellor (University of Nottingham), Daniele Muraro (University of Nottingham), Leah Band (University of Nottingham)

Multicellular organisms comprise many different and highly specialized cell types arranged in specific patterns in space and time. The formation of pattern is encoded in genetic and environmental responses. All multicellular organisms start as a single cell. This cell and its daughter cells divide to produce new cells. These divisions are highly orchestrated and both division and growth occur asymmetrically.Plant cells are locked into place by substantial cell walls. All these cells have the same genetic information and positional cues are required to assign specific identities to cells in defined positions. Roots provide an ideal system to investigate cellular pattern as cells are arranged in well-defined lineages extending out of an organised centre.During embryogenesis, cells in the embryonic root are arranged in a radially symmetric pattern of concentric rings. However, as the seedling grows new cell fates (xylem and phloem) are assigned in the central part of the root to transport water and nutrients throughout the plants. The differentiation of these transporting cells represents a crude symmetry breakage with a shift from radial to bisymmetry (two planes of symmetry at 90º to each other).A network of interactions able to produce this symmetry break will be presented. Experimental evidence demonstrating the involvement of these components will be presented and a mathematical model that predicts how these components act in space and time to produce pattern will be described. How this network can be manipulated to produce alternative patterns will also be noted.
CGPW02 18th September 2015
16:15 to 17:00
John Dallon Streaming in Dd and Cell-cell adhesions
Results from two mathematical models will be discussed. In the first, contradictions between experiments and modeling in Dictyostelium discoideum will be addressed. Experiments suggest that streaming in early aggregation is dependent on localization of certain proteins (ACA) in the cell. Yet mathematical modeling seems to contradict this result. In the second model, the role of cadherin motion in the cell membrane will be studied to determine how it affects cell-cell adhesion lengths. Using the immersed boundary method, the cell membrane and cortex is modeled. The model is used to help determine what role the actin cytoskeleton plays in cell-cell adhesion.
CGP 29th September 2015
11:00 to 12:30
Numerical methods for large bilayer bending problems
Thin elastic bilayer structures arise in various modern applications, e.g., in the fabrication of nanotubes or microgrippers. The mathematical modeling leads to a nonlinear fourth order problem with nonlinear pointwise constraint. We prove the convergence of a finite element discretization within the framework of $\Gamma$-convergence and discuss the convergence of an iterative solution method.
CGP 1st October 2015
11:00 to 12:30
Parallel multigrid methods for parabolic partial differential equations and applications
In the first part of the talk, I will give the audience an overview of a so-called geometric multigrid. I must extend the discussion to include advanced computational techniques for better efficiency, namely adaptive mesh refinements, parallelisation through domain decomposition and adaptive time-stepping.

In the second part, I will describe how do we apply these techniques to mathematical models of partial differential equations. We will have a look at a thin film model of droplet spreading. Then we move on to an optimal control model for whole cell tracking. I will also discuss some robust techniques of greater efficiency for general semi-linear optimal control models. The whole cell tracking is closely related to the cell biology and I hope to end the talk with some discussions to its further practical use.

CGP 6th October 2015
11:00 to 12:30
RK Upadhyay Spatiotemporal transmission dynamics of recent Ebola spread and outbreak in West Africa: impact of control measures
Recently, the 2014 Ebola virus (EBOV) outbreak in West Africa is the largest outbreak to date. To understand the Ebola transmission dynamics, we formulate a compartmental epidemic model with exponentially decaying transmission rates and study the impact of control measures to basic public health using an SEIR model. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and studied the spatial spread of the epidemic via reaction-diffusion modeling. We do not fit the model to the observed pattern of spread rather, we use parameter values estimated in past and examine the extent to which the designed model prediction agrees with the pattern of spread seen in Guinea, Liberia and Sierra Leone, West Africa. We employ disease threshold and sensitivity analysis to determine the extent to which the predictions could have improved by better parameterization.

Numerical simulations are performed with and without control measure for the designed model system. Using central manifold theory, it is established that the transcritical bifurcation occurs when basic reproduction number passes through unity. The proposed Ebola epidemic model provides an estimate to the potential number of future cases. The model indicates that the disease will decline after peaking up if multisectorial and multinational efforts to control the spread of infection are maintained. Possible implication of the results for disease eradication and its control are discussed which suggests that proper control strategies like: (i) transmission precautions, (ii) isolation and care of infectious Ebola patients, (iii) safe burial, (iv) contact tracing with follow-up and quarantine, and (v) early diagnosis are needed to stop the recurrent outbreak. A significant reduction in infection and death cases are observed when proper control measures after two months is incorporated in the model system. Two dimensional simulation experiments show that infectious population and the number of deaths in Sierra Leone will increase up to one and a half year without control but it will decline after two years. So there is a hope to end this disaster.

Keywords Ebola epidemic model; Transcritical bifurcation; Spatial spread; Basic reproduction number; Control measures.

CGP 8th October 2015
11:00 to 12:30
The structure and logic of axis extension in Drosophila
Convergence and extension movements are evolutionarily conserved morphogenetic behaviours that elongate tissues in many contexts in animal embryogenesis and organogenesis. Drosophila germ-band extension is a well-studied example that deforms the germ-band epithelium, a thin monolayer of cells tesselating the surface of the ellipsoidal embryo. Extension is driven by the combination of two temporally coordinated mechanisms. A pull from the posterior of the embryo drives extension of the tissue towards the posterior. Meanwhile, a planar polarised distribution of actin and Myosin II motors drives active cell rearrangements within the tissue, driving convergence in the dorso-ventral axis.

Our initial work focused on precise descriptions of cell behavioral dynamics in the germ-band epithelium, for which we developed automated cell tracking and 2D tensorial methods to quantify tissue and cell shape deformation rates, from which a cell rearrangement tensor could be derived1. Tissue deformation is dominated by cell rearrangements and cell shape change, since there is no growth in this tissue and cell divisions don't contribute until late on. Having quantified strains in detail we set about inferring the likely stresses causing our observed strain patterns. Gradients of cell shape stretch and area increase showed that a posterior pull was likely to drive the initial fast phase of extension2, and we have recently shown that this is driven by the posterior mid-gut invagination3.

There were also intriguing periodicities along the anterior-posterior (AP) embryonic axis in the rate of cell intercalation, so in recent work we have been analysing the temporal dynamics of Myosin II polarization, responsible for intrinsic stresses, to understand this pattern formation. We confirm that at the onset of germ-band extension, Myosin II is enriched at AP cell-cell interfaces. As the tissue extends due to cell intercalation, increasing the number of cells in AP, enrichment emerges at boundaries every two to three cells along the AP embryonic axis. Myosin II is localized at boundary interfaces and not the intervening interfaces, irrespective of interface orientation, arguing against the role of global signals. Furthermore, we show that polarized cell rearrangements occur primarily at these boundaries. Myosin II-enriched boundaries therefore provide a single mechanism for simultaneously limiting cell intermingling and driving cell rearrangements during axis extension. Finally, I will speculate on the logic of the combinatorial gene expression code that generates robust periodic Myosin II patterns.

1Blanchard et al., 2009, Nature Methods 2Butler et al., 2009, Nature Cell Biology 3Lye et al., 2015, PLOS Biology (accepted)

CGP 13th October 2015
11:00 to 12:30
Morphogenetic models: from genetic regulatory networks to phenotypes
We consider the space-time dynamics given by a genetic regulatory network for the cell fate determination during flower development. Starting with experimental data, we construct a dynamical system that recovers wild type as well as mutant phenotypes. We extend this to a reaction-diffusion system that provides a model that accounts for the spatial architecture of the flower. We discuss how this approach can be generalised to other systems in developmental biology and also comment on open questions, both biological and mathematical.
CGP 15th October 2015
11:00 to 12:00
Anomalous diffusion is everywhere but where?
It has become clear that anomalous diffusion is as widespread and important as normal diffusion. However, in biological systems anomalous diffusion is usually observed as a transient before transition to normal diffusion. In my talk I will describe an approach to non-linear and non-Markovian generalization of two popular models of anomalous diffusion: subdiffusive continuous time random walk and superdiffusive Levy walk model. This approach easily allows to take into account external forces and interactions between random walkers. More importantly, we show that external forces and interactions lead to the transition to seemingly normal diffusion. This may lead to a wrong conclusion in analyses of experimental results on transient subdiffusion. Contrary to normal diffusion, the properties of the process remain to depend on anomalous exponent.
CGP 20th October 2015
11:00 to 12:00
Finite element methods in geometric integration
Geometric integration is the study of numerical schemes which inherit some property from the continuum limit they approximate. In this talk we examine the role of finite element temporal discretisations of some model ODE problems, moving onto how they can be applied in semi and fully discrete numerical schemes for PDEs. The specific model we illustrate in this talk is the Navier-Stokes-Korteweg equation which is a diffuse interface phase field model
CGP 22nd October 2015
09:00 to 10:00
Our "second brain": modelling its development and disease
The enteric nervous system (ENS) in our gastrointestinal tract, nicknamed the second brain'', is responsible for normal gut function and peristaltic contraction. Embryonic development of the ENS involves the colonisation of the gut wall from one end to the other by a population of proliferating neural crest cells. Failure of these cells to invade the whole gut results in the relatively common, potentially fatal condition known as Hirschsprung's disease. We have collaborated with developmental biologists for over ten years, addressing various aspects of ENS development and disease. Both continuum and discrete models have provided insight into the key biological processes required for complete colonisation and have generated experimentally testable predictions.
CGP 27th October 2015
11:00 to 12:30
Hydrodynamic diffuse interface models for Helfrich and mean curvature flow and their application to cells in fluid environment
Helfrich and mean curvature flow are widely used to describe the physics of cell membranes. In this talk I will show how such hydrodynamic models can be derived and coupled to additional physical effects such as reaction-diffusion kinetics, liquid crystals or the interaction of multiple cells. We will apply these models to numerically simulate cell motility and white blood cell margination.
CGP 29th October 2015
11:00 to 12:30
Formation and regulation of filopodia
Filopodia are finger-like actin-rich protrusions from cells and their number, length and turnover rates are important for their functions. Their roles are as diverse as direction sensing by neuronal growth cone filopodia, targeting signaling during morphogenesis by cytonemes, and detecting sound through the stereocilia in the ear. We are using a two-pronged approach to elucidate the molecular basis of filopodia formation: in vivo imaging of filopodia in developing Drosophila and a cell-free system of filopodia-like structures.

Drosophila embryos display similar phases of differentiation and movement to vertebrate muscles. In addition, development is external (unlike mammals), live in vivo imaging is experimentally tractable, there is a wide molecular biology and genetic toolkit, and Drosophila typically have less redundancy in gene isoforms compared to vertebrates. Timelapse confocal imaging of developing muscles in Drosophila shows intense filopodial activity during migration which diminishes as the muscles attaches to tendon cells in the epidermis. We show that integrins localise to these filopodia and signaling through integrins controls filopodia length and dynamics, which, in turn is needed for the arrest of migration when muscles reach tendon cell attachment sites.

The cell-free system uses PI(4,5)P2-containing supported lipid bilayers as a plasma membrane mimic and frog egg extracts are used to mimic cytosol. Adding extracts to the supported lipid bilayers causes the nucleation of actin foci on the surface and the growth of long actin bundles up from the surface. The cell-free system offers the ability to subtract and add back extracts, fractions of extracts and purified proteins, and is highly amenable to microscopy. We have found that initiation, but not elongation, of filopodia-like structures is driven by formation of the stable tip complex of actin regulators. Elongation is driven by dynamic proteins that are in exchange with the tip complex.

This combination of biochemical dissection, microscopy and genetics allows us to elucidate how developmental programs and membrane environment control actin regulators to orchestrate cell architecture and dynamics.

CGP 3rd November 2015
10:00 to 11:00
The mechanobiology of adipocytes
CGP 3rd November 2015
11:00 to 12:00
Cell-based modelling for wound contraction and angiogenesis
Wound contraction and angiogenesis are biological processes that often take place during healing of wounds and in tumor development. To model these processes, one distinguishes between different types of models, which are descriptive at several scales, ranging from cellular scale (micro-scale) to the tissue scale (macro-scale). The models are on the macro-scale are based on continuum hypotheses, which means that one sets up and solves partial differential equations with the associated boundary and initial conditions. On the smallest scale one models all kinds of cell phenomena on a molecular level. In this talk, we will consider colonies of cells, which are treated as discrete entities, as well as chemical and mechanical signals that are modelled as sets of partial differential equations. Hence, the current approach is a hybride one.

The process of angiogenesis, which is the formation of a vascular network in tissues, is often modeled by using principles based on cell densities in a continuum approach or on hybride cellular-continuum level where one uses cellular automata (in particular cellular Potts) models. In this study, we abandon the lattice needed to model the cell positions in cellular automata modelling and instead, we apply a continuous cell-based approach to simulate three-dimensional angiogenesis. Next to the application of this modelling strategy to angiogenesis, we discuss the application of the formalism to wound contraction.

The talk will describe some of the mathematical issues encountered in these models and further some animations will be shown to illustrate the potential merits of our approaches.

CGP 10th November 2015
11:00 to 12:30
Mathematical modelling of a cereal killer: Modelling plant cell invasion by the rice blast fungus
We present a mathematical model for plant cell invasion by the rice blast fungus. The model couples an evolution law for the growth of a tumour on the plant leaf to a reaction diffusion system that holds on the surface of the tumour. We derive a finite element approximation to the model and we show some computational results.
CGP 12th November 2015
11:00 to 12:30
Modelling and simulation of elastic cells in flow
Accurate measurements of cell elasticity help doctors and biologists to detect diseases and physiological changes of biological cells. An innovative new technique uses a flow scenario to measure the elasticity of large amounts of cells at a rate of 100 cells per second. The idea is to flow cells through a narrow channel which leads to deformation by shear stress and pressure gradients. A comparison of the observed cell shapes with numerical simulation results permits conclusions on the elasticity of the cell.

In my talk I will address numerical methods to simulate this scenario. In particular I will present three different modeling approaches for cells flowing through a narrow channel, where cells are modeled either as

(i) viscous fluids with surface tension to account for actomyosin contraction of the cytoskeleton, (ii) viscoelastic bodies to account for the viscoelasticity of intracellular components, (iii) fluid-filled elastic shells accounting for the elasticity of the cytoskeleton.

A phase field is used in all three approaches to represent the cell geometry which permits an easy mechanism to couple the cell geometry to additional equations for elasticity and surface tension. I will compare the obtained cell shapes with experimental and analytical results and draw conclusions on which the model is best-suited to describe biological cells in flow.

CGP 17th November 2015
11:00 to 12:30
A hybrid model to test mechanical cues driving cell migration in angiogenesis
Many studies are stressing the crucial importance of the mechanical component in angiogenesis, but still, very few models really integrate mechanics. We propose to investigate the importance of mechanical cues for cell migration in this context with a new hybrid continuous-discrete model that describes the individual migration of contracting cells on an elastic matrix of fibres. The matrix is described as a continuum whereas the cells are described as discrete elements.
CGP 19th November 2015
11:00 to 12:30
Contortion of a beach ball
Touching an object is not always necessary to evaluate its mechanical properties. Similarly, obtaining clues on a microscopic structure can be done without the use of sophisticated devices : in some cases, the simple observation of a shape can tell a lot.

In the research domain of Soft Matter, many nice shapes can be met, taken by very deformable objects under weak sollicitations, that are to be interpretated with quite simple concepts (surface tension, entropy, elasticity...). In this respect, beach balls and their cousins are efficient models for several objects of Soft Matter, because they present a variety of qualitatively different behaviours when they undergo deflation. After a short introduction to surface mechanics, I will present how these type situations can explain some aspects of more elaborated systems (like the efficiency of the trap to be found in some carnivorous plants), or guide the realization of artificial microswimmers designed to be remotely controlled in the human body through echographic

CGP 19th November 2015
16:00 to 17:00
S Etienne-Manneville Keeping in contact during collective cell migration
Collective cell migration is essential during development as well as in adult organisms where it participates, for instance, in tissue renewal, wound healing or cancer invasion and metastasis. As cells migrate collectively, intercellular junctions maintain the integrity of the cell monolayer while allowing differential movement and rearrangements of adjacent cells. In astrocytes, intercellular contacts are mainly formed by N-cadherin-mediated adherens junctions. Downregulation of N-cadherin is frequently observed in astrocyte derived tumors, gliomas and promotes single cell migration while perturbing cell polarity and increasing cell velocity.

To understand how cells can maintain stable intercellular junctions and simultaneously rearrange them to accommodate cellular displacement, we have investigated cadherin dynamics during astrocyte collective migration. We show adherens junctions undergo a continuous retrograde movement compensated by a polarized recycling of cadherin from the rear to the leading edge. Such dynamics allows the cells to maintain stable contacts while permitting changes of cellular interactions. In glioma cells, N-cadherin dynamics and consequently the maintenance of cell-cell contacts are perturbed leading to loss of cell polarity and to increased migration.

CGP 24th November 2015
11:00 to 12:30
Discrete and continuous modelling of cell mechanics: from adhesion to migration
The talk is devoted to two different approaches to model and simulate processes occurring during cell migration. Firstly, a discrete computational model in 3D is presented to simulate the formation of cell-matrix adhesions on a single 3D matrix fibre. This model allows to analyse the importance of the alignment between the matrix fibre and the cell protrusion on the size of the focal adhesions. Secondly, a 1D multi-physics model of fluid-structure interaction to simulate the behaviour of a cell confined in a complex microfluidics device is introduced. Cells are modelled as a poroelastic material following recent experimental evidences whereas the fluid is modelled by using the Poiseuille equation, considering it as a laminar incompressible Newtonian fluid.
CGP 26th November 2015
11:00 to 12:30
A Bayesian approach to parameter identification in Turing systems
We present a methodology to identify parameters in Turing systems from noisy data. The Bayesian framework provides a rigorous interpretation of the prior knowledge and the noise, resulting in an approximation of the full probability distribution for the parameters, given the data. Although the numerical approximation of the full probability distribution is computationally expensive, parallelised algorithms produce good approximations in a few hours. With the probability distribution at hand, it is straightforward to compute credible regions for the parameters. The methodology is applied to a well-known Turing system: the Schnakenberg system.
CGP 1st December 2015
11:00 to 12:30
Regulation of actin assembly and mechanotransduction in cell-matrix adhesion complexes: a biochemical study of the talin-vinculin complex
Cell migration is involved in many physiological and pathological processes. Force is produced by the growth and the contraction of the actin cytoskeleton (1). To produce force in adherent cells, these actin networks must be anchored to the extracellular matrix (ECM) by adhesion complexes (1,2). These structures contain transmembrane integrins that mechanically couple the ECM to the intracellular actin cytoskeleton via actin binding proteins (ABPs) (2). This system acts as a molecular clutch that controls force transmission across adhesion complexes. This molecular clutch is a complex interface made of multiple layers of regulated protein-protein interactions (2). The multiple activities of the ABPs present in these structures play a critical role in the dynamics of this interface. In addition to the control of actin filament binding and polymerization (1-3), these proteins sense and respond to the force applied by the actomyosin cytoskeleton to adjust the anchoring strength (4,5). Our goal is to determine the molecular mechanisms by which these ABPs cooperate to control the mechanical coupling between the actin cytoskeleton and cell-matrix adhesion complexes.

To study these ABPs, our laboratory combines the measurement of actin polymerisation kinetics using fluorescence spectroscopy, single actin filament observations using TIRF microscopy and the reconstitution of actin-based mechanosensitive processes on micropatterned surfaces. Our model system is the mechanosensitive complex made of the two ABPs talin and vinculin.

Our results showed that vinculin controls actin filament elongation (3). More recent results revealed that talin also regulates actin polymerisation in response to integrin binding (unpublished data). In addition, we have developed a microscopy assay with pure proteins in which the self-assembly of actomyosin cables controls the association of vinculin to a talin-micropatterned surface in a reversible manner (4, 5). This in vitro reconstitution revealed the mechanism by which a key mechanosensitive molecular switch senses and controls the connection between adhesion complexes and the actomyosin cytoskeleton.

CGPW04 7th December 2015
10:00 to 11:00
Mark Chaplain Mathematical modelling of angiogenesis in wounds, tumours and retinae: The good, the bad and the beautiful
Angiogenesis is the growth of a new network of blood vessels from a pre-existing vasculature. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration and proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. Angiogenesis is a vital component of both normal and pathological processes such as wound healing, solid tumour growth and retinal development.

In this talk we will present a basic mathematical model for the development of a vascular network which simultaneously couples vessel growth with blood flow through the vessels - a dynamic adaptive vasculature model. We will then apply the model to three different biological scenarios: (i) tumour-induced angiogenesis; (ii) wound healing and (iii) the developing retina. The computational simulation results will be compared with experimental data and the predictions of the model discussed with regard to scheduling of the delivery of chemotherapy drugs to solid tumours.
CGPW04 7th December 2015
11:30 to 12:30
Daphne Weihs Making Holes: Identifying How Metastatic Cancer Cells Apply Force to Invade Their Microenvironment
The process of invasion is of special importance in cancer metastasis, the main cause of death in cancer patients. Cells typically penetrate a matrix by degrading it or by squeezing through pores. However, cell mechanics and forces applied by cells especially during the initial stages of metastatic penetration, as metastatic cells indent a substrate, are still unknown. We measure the forces that cells apply to an impenetrable, synthetic 2-dimensional gel-matrix, effectively limiting cells to rely only on mechanical-interactions; gels are non-degradable polyacrylamide with sub-micron pores. We show that single metastatic breast-cancer cells will apply force to an impenetrable gel, and indent it in attempted invasion, when the gel is in the appropriate stiffness range; benign cells do not indent the gels. The metastatic cells require gel-substrates to be soft enough to indent, yet stiff enough to grip and generate force on. Cells develop grip handles and pull the underlying gel s inwards and upwards bringing the nucleus into the indentation concavity. We reveal a special coordinated role for the nucleus and the cytoskeleton when a single cell attempts to invade the impenetrable barrier. The actin, nucleus, and microtubules reorganize in sequence, with the actin at the leading edge of the cell. Cells repeatedly attempt penetration over several hours and then relocate, indicating an advanced mechano-transduction feedback loop. We use finite element analysis to identify force application patterns to maximize indentations, by varying cell size, shape and the locations and magnitudes of the mechanical loads applied by cells. We demonstrate that cells must combine lateral forces and significant normal forces to achieve the large, experimentally observed gel-indentations. The systems and analysis approaches shown here reveal cell adaptability and force application mechanisms.

CGPW04 7th December 2015
13:30 to 14:15
Stéphanou Angélique An integrated computational approach for the design of patient-specific virtual tumours
The design of a patient-specific virtual tumour is an important step towards personalized medicine since the virtual tumour can be used to define the most adapted and efficient treatment protocol. However this requires to capture the description of many key events of tumour development, including angiogenesis, matrix remodelling, hypoxia, cell heterogeneity that will all influence the tumour growth kinetics and degree of tumour invasiveness. To that end, an integrated hybrid and multiscale approach has been developed based on data acquired on a preclinical mouse model as a proof of concept. Fluorescence imaging is exploited to build case-specific virtual tumours and to validate their spatiotemporal evolution. The validity of the model will be discussed as well as its potential to identify the best therapeutic strategy for each individual tumour case.
CGPW04 7th December 2015
14:15 to 15:00
Amit Gefen The structural integrity of cells under sustained mechanical deformations: The key for understanding pressure ulcers
Sustained internal mechanical loads in tissues which develop during immobile weight-bearing postures such as while in bed or in a chair were identified as a fundamental cause for the onset and progression of pressure ulcers (PUs), particularly of the deep tissue injury (DTI) type. The sustained loading may compromise tissue viability either directly, by distorting cell shapes, or indirectly, by distorting the vasculature or lymphatic networks or, at the micro-scale, by distorting cellular organelles involved in regulating transport, e.g. the plasma membrane (PM). This talk will review our record of published research concerning the effects of sustained deformations across the different hierarchical scales: tissue-scale [cm], meso-scale [mm] and cell-scale [μm], with a focus on how sustained bodyweight loads eventually compromise homeostasis and cell viability. The evolution of our work to test our central hypothesis will be shown, specifically, that macroscopic tissue defo rmations translate to cell-level deformations and in particular, to localized tensile strains in the plasma membrane (PM) of cells. These localized PM stretches increase the permeability of the PM which, over time, could disrupt vital transport processes such as the function of ion channels, endocytosis and exocytosis. Viability of tissues exposed to sustained loading in the context of pressure ulcer development should therefore be investigated in all dimensional scales, from the macro to micro, and in particular at a cell scale, in order to provide complete understanding of the aetiology of PUs and DTIs and for identifying individuals for whom and conditions at which the susceptibility to these injuries might be greater. Emerging relevant methods of cell permeability quantification and modeling such as multiscale and multiphysics modeling will be highlighted, as they contribute substantially to the aetiological research in this field.
CGPW04 7th December 2015
15:30 to 16:15
Dumitru Trucu Structured Models of Cell Migration Incorporating Membrane Reactions
The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes enables a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this work we establish a general spatio-temporal-structural framework that enables the description of surface- bound reaction processes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two concrete examples arising from cancer invasion.
CGPW04 7th December 2015
16:15 to 17:00
Dagmar Iber From Networks to Function – Computational Models of Organogenesis
One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks ­and how do they evolve? Morphogenesis provides an excellent model system to study how simple molecular networks robustly control complex pattern forming processes on the macroscopic scale in spite of molecular noise, and how important functional variants can evolve from small genetic changes. Recent advances in 3D imaging technologies, computer algorithms, and computer power now allow us to develop and analyse increasingly realistic models of biological control. In my talk, I will show how data-based modelling can be used to define mechanisms for fundamental developmental processes and I will discuss the computational challenges that arise.
CGPW04 8th December 2015
09:00 to 10:00
Alan Champneys Turing bifurcation, wave-pinning or localised patterns for cell polarity formation; three sides of the same coin?
In this talk I shall present recent work in collaboration with students Nicolas Verschuren and with Victor Brena motivated by problems of cellular level polarity formation motivated by a range of problems in plant biology. After reviewing some existing theories based on reaction-diffusion modelling, I will present some work on plant root hair formation in Arabidopsis in collaboration with Claire Grierson. By modelling the kinetics of the plant rho proteins, or ROPs, it will be argued that the key mechanism can be explained by the formation of a localised patch, which arises due to the presence of a subcritical Turing bifurcation and the recent theory of so-called homoclinic snaking. To see what happens in wild type, one needs to include spatial gradients, such that the dynamics of the patch can be explained asymptotically with the help of Michael Ward's semi-strong analysis technique. The mechanism is contrasted with that of the recent theory of wave pinning in mass-conservative reaction-diffusion equations. It is argued that small source and loss terms are biologically motivated by actions of the nucleus controlling the process and by proteins being recycled as symmetry-breaking takes hold. A new study is then undertaken of what happens under introduction of small source and loss terms to a canonical wave-pinning model. It is shown that localised patterns develop into snakes in one limit and in other limit develop into pinned fronts. A new asymptotic analysis shows how front selection occurs in the limit that the source and loss terms tend to zero.
CGPW04 8th December 2015
10:00 to 11:00
Chandrasekhar Venkataraman Free Boundary Problems from a Model for Receptor-Ligand Dynamics
Co-authors: Charles Elliott (Warwick), Thomas Ranner (Leeds)

We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling that models receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the ECM.

We prove the existence and uniqueness of a solution to the model and we also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to the limiting problems, which take the form of free boundary problems posed on the cell surface. We also present numerical simulations in a realistic geometry.
CGPW04 8th December 2015
11:30 to 12:30
Fred Vermolen Cell-Based Modelling of Wound Contraction, the Immune System and Angiogenesis
Wound contraction and angiogenesis are biological processes that often take place during healing of wounds and in tumor development. To model these processes, one distinguishes between different types of models, which are descriptive at several scales, ranging from cellular scale (micro-scale) to the tissue scale (macro-scale). The models are on the macro-scale are based on continuum hypotheses, which means that one sets up and solves partial differential equations with the associated boundary and initial conditions. On the smallest scale one models all kinds of cell phenomena on a molecular level. In this talk, we will consider colonies of cells, which are treated as discrete entities, as well as chemical and mechanical signals that are modelled as sets of partial differential equations. Hence, the current approach is a hybride one.

The process of angiogenesis, which is the formation of a vascular network in tissues, is often modeled by using principles based on cell densities in a continuum approach or on hybride cellular-continuum level where one uses cellular automata (in particular cellular Potts) models. In this study, we abandon the lattice needed to model the cell positions in cellular automata modelling and instead, we apply a continuous cell-based approach to simulate three-dimensional angiogenesis. Next to the application of this modelling strategy to angiogenesis, we discuss the application of the formalism to wound contraction.

Next to angiogenesis, a cell deformation and migration model will be presented, where the cell boundary, as well as the boundary of the nucleus is divided into a set of discrete points. Cell migration is modelled in terms of random walk and chemotaxis. The deformation of the nucleus is a novel step in literature.

The talk will describe some of the mathematical issues encountered in these models and further some animations will be shown to illustrate the potential merits of our approaches.
CGPW04 8th December 2015
13:30 to 14:15
Alexander Hunt DTI-Based Multiscale Modelling of Glioma
Co-Authors: C. Surulescu (TU Kaiserslautern), C. Engwer (WWU Munster)

Glioma invasion is a multiscale process ranging from subcellular biolo- gical events to the growth of a solid tumour mass. Key features involved in this process are migration and proliferation. The former is modelled using kinetic transport equations including medical data, which reveal the brain structure in detail. For characterising proliferation we use two alternative approaches: one relying on the go-or-growth dichotomy and involving two tumour cell populations, and the other paying attention to cell-tissue interactions seen as the onset of the biological processes leading to cell division.

For the biomedical application it is interesting to also include some therapy approach. We propose a new model combining receptor binding inhibition with radiation therapy and perform numerical simulations for the di
erent settings.
CGPW04 8th December 2015
14:15 to 15:00
Nikolaos Sfakianakis Filament Based Lamellipodium Model (FBLM) modeling and numerical simulations
The cytoskeleton is a cellular skeleton inside the cytoplasm of living cells. The front of the cytoskeleton, also known as lamellipodium and is the driving mechanism of cell motility and is comprised by long double helix polymers of actin protein termed actin-filaments. The actin-filaments polymerize/depolymerize and exhibit a series of physical properties like elasticity, friction with the substrate, crosslink binding, repulsion, myosin-drive contractility, nucleation, fragmentation, capping and more.

In this talk we address the FBLM that describes the above (microspcopic) dynamics of the actin-filaments and results to the (macroscopic) movement of the cell. We introduce the Finite Element Method (FEM) used to simulate this system and present numerical experiments exhibiting the motility of the cells in a series biological scenaria (including chemotactic and haptotactic influence) and compare our results with on-vitro experiments.

Joint work(-s) with Chr. Schmeiser, D. Oelz, A. Manhart, V. Small

CGPW04 8th December 2015
15:30 to 16:15
Natalie Emken A continuous reaction-diffusion-advection model for the establishment of actin-mediated polarity in yeast
Co-author: Prof. Dr. Christian Engwer (Institute for Computational and Applied Mathematics, University of Muenster)
Cell polarity plays a crucial role for many different cell types. In the yeast cell, the model system to study the underlying mechanisms of polarization, the GTPase Cdc42 is a key regulator of this process. Its clustering relies on multiple parallel acting mechanisms. A common model explains polarity by a Turing-type mechanism. Based on reaction-diffusion equations it simulates a Bem1-mediated Cdc42 recruitment. Since cell polarity occurs even in the absence of Bem1, recent papers emphasize the exchange between the cytosol and the plasma membrane. However, studies combining biological experiments and mathematical simulations also suggest an actin-mediated feedback of Cdc42. Stochastic vesicle trafficking models demonstrate that transport of Cdc42 via actin cables can either reinforce or perturb polarization . We present a minimal mathematical model, based on reaction-diffusion-advection equations, that is able to reproduce the experimentally observed phenomena, in particular those of knock-down experiments. Contrary to former approaches which only incorporate the diffusive transport, our system explicitly simulates exocytosis and endocytosis of Cdc42. Vesicles move along actin cables, thus we further consider actin polymerization and depolymerization. Since we consider five substances, either cytosolic or membrane-bound, and model the full geometry we have a coupled bulk-surface problem. We present numerical results in 3D and compare those to experimental data. This way, we show that the model is able to reproduce experimentally observed pathological cases and demonstrate how vesicle transport could reinforce polarity. Based on this specific model, we develop a general system of three membrane reaction-diffusion equations coupled to two diffusion equations inside the cell. We perform a linearized stability analysis and derive conditions for a transport-mediated instability. We complete our theoretical analysis by numerical simulations for different geometries.
CGPW04 8th December 2015
16:15 to 17:00
Rachel Bearon Continuum models for motile cells in shear flow
Many micro-organisms such as bacteria and algae swim in fluid environments. This swimming behaviour can interact with fluid motions to generate transport which differs both from that experienced by passive tracers in flow and micro-swimmers in the absence of flow. I will give examples of how population-level models can be derived to describe the spatio-temporal distribution of such swimmers, including a model for slender bacteria which undergo run-and-tumble chemotaxis in a channel (Bearon et al J. Fluid Mech. 2015). The continuum model developed can describe an experimentally observed phenomenon of trapping in high shear which existing drift-diffusion models are unable to capture.
CGPW04 9th December 2015
09:00 to 10:00
Veronica Grieneisen Multilevel approach to cell and tissue polarity and traffic jams
In this talk I wish to compare and contrast cell and tissue polarity between very diverse organisms. Computational approaches combined with molecular studies and in vivo microscopy were necessary to reveal how polarity is coordinated and linked on three different levels: on the scale of the tissue, the cellular and subcellular tissue level. At the single cell level, a spatially uniform activation and patterning of GTPases can cause polarity to emerge spontaneously, independent of spatial pre-patterns or localized polarizing signals. We argue that plants and animals have inherited this same “unicellular mode” of establishing cell polarity, and that multicellular coordination has thereafter diverged using this underlying mechanism as a building block: Being capable of intracellular partitioning, neighbouring plant cells that are separated by cell wall then coordinate their polarities - through indirect cell-cell coupling. This is resultant from changes in concentration level of a phytohormone, auxin, inbetween and along cells.

In the specific case of pavement cells of leaves (jigsaw-shaped cells with interlocking lobes and indentations), this phenomenon comes about as interdigitation, and requires the opposite response of identical neighbouring cells to the same local auxin signal in the cell wall, between the cells. Our theoretical work identifies key requirements for such indirect cell-cell signalling that that gives rise to correct interdigitation. These requirements, based on known molecular interactions, can then be extrapolated to other multi-cellular tissues, to understand the interdependency between cell and tissue polarity.

Extrapolating these findings we further show how animal cells, capable of direct cell-cell coupling, can establish, through similar principles, robust tissue coordination. In the end of our talk, I will also show how established tissue polarity in plants requires extra conditions of regulation, to avoid issues of traffic jam in relation to nutrient uptake.

CGPW04 9th December 2015
10:00 to 11:00
Yasin Dagdas Membrane remodeling and cellular morphogenesis during plant tissue colonization
One of the biggest challenges of 21st century is feeding the growing human population. Plant pathogens cause devastating yield losses in staple crops and pose a serious threat to global food security. According to recent reports, plant pathogens cause crop losses that if alleviated would feed at least 700 million people. To prevent crop loses due to pathogens, we have to understand plant-microbe interactions at molecular and systems level. To facilitate plant colonization these deadly microbes evolved unique infection strategies. They form specialized infection cells that involve tightly controlled spatiotemporal repolarization events. Additionally, pathogens also induce extensive membrane remodeling within plant tissues. They initiate plant infection via invagination of plant plasma membrane and reorient cellular resources to these infection cells. They can occupy up to 80% of plant cell volume without inducing any immune response. We have limited knowledge on the molecular details of infection cell morphogenesis and cellular reprogramming during plant infection. I will present our recent results on rice blast and Irish potato famine pathogen and propose research questions that can be answered using mathematical modeling.
CGPW04 9th December 2015
11:30 to 12:30
Angela Stevens Stochastic particle models and chemotactic/haptotactic motion of cells
Co-authors: Stefan Grosskinsky (University of Warwick), Daniel Marahrens (formerly MPI MIS Leipzig), Juan Velazquez (University of Bonn)

In this talk the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive chemical molecules on a finite number of lattice sites. They interact directly among themselves only on the same lattice site. The chemical environment is assumed to be stationary with a slowly varying mean, which results in a non-trivial macroscopic chemotaxis equation for the cells. Methodologically the limiting procedure and its proofs are based on results by Koukkous and Kipnis/Landim. Further PDE-ODE based haptotaxis models are discussed and their relation to attractive reinforced random walks.
CGPW04 9th December 2015
13:45 to 14:30
Mark Chaplain Case Studies in Cancer Modelling
CGPW04 9th December 2015
14:30 to 15:00
Neil Dalchau Systems Biology Research at Microsoft
CGPW04 9th December 2015
15:20 to 15:50
Jamie Meredith Grand Challenge and Other Funding Opportunities at Cancer Research UK
CGPW04 9th December 2015
15:50 to 16:20
Jonathan Stott Quantitative Biology Research at Astra Zeneca
CGPW04 10th December 2015
09:00 to 10:00
Katarina Wolf Principles of single and collective cancer cell migration: Impact by environmental substrate guidance
The migration of single cells or cell collectives in the multicellular organism is a complex process that takes place during a wide range of physiological functions in the organism, as well as during disease, such as cancer. Cell migration takes mainly place within complex extracellular matrix (ECM) environments of different dimensionality, structure, and spacing. Hence basic concepts on cell migration have been extended from 2D into the 3D context. Examples will be shown on how mesenchymal, amoeboid or collective migration modes are maintained or modulated by the tissue architecture in vitro as well as in vivo.
CGPW04 10th December 2015
10:00 to 11:00
Luigi Preziosi Multiscale modelling for cell motility
Several problems regarding cell motility and morphogenesis are characterized by the contemporary presence of cells that behave as single entities and cells that follow and cluster around them. From the mathematical point of view, describing such phenomena requires the development of mathematical models in which virtual cells can switch from a discrete to a continuous description. Keeping this in mind, the talk aims at presenting some ideas on how to do that, making for instance use of measure theory or introducing the concept of bubble functions.
CGPW04 10th December 2015
11:30 to 12:30
Pierre Degond Modelling of cross-linked fiber networks and tissue self-organization
In this talk, we will derive a continuum model for the dynamics of a network of cross-linked fibers. We will outline how this model can be applied to the modelling of tissue self-organization.
CGPW04 10th December 2015
13:30 to 14:15
Niklas Kolbe Mathematical modelling and simulation of an Epithelial-Mesenchymal-like transition in cancer cells
Recent biological work has revealed the existence of cells within the body of a tumour that differ in their level of differentiation from the bulk of the cancer cells. Compared to the more usual differentiated cancer cells, these cancer stem cells exhibit higher motility, they are more resilient to therapy, and are able to metastasise to secondary locations within the organism. They seem to transition from the differentiated cancer cells via a (de-)differentiation program, termed Epithelial-Mesenchymal Transition, which can also be found in normal tissue. The compound of the tumour as well as its internal dynamics affect the extracellular environment, in particular the invasion of the Extracellular Matrix.

In this talk we introduce a model that combines the transition between the afore-mentioned types of cancer cells based on the (microscopic) dynamics of the Epidermal Growth Factors, with the (macroscopic) invasion of the Extracellular Matrix by the cancer cell ensemble. Moreover, we present numerical experiments exhibiting the dynamics of both types of cancer cells and elaborate on the numerical methods that we use.

[1] N. Hellmann, N. Kolbe, N. Sfakianakis: A mathematical insight in the epithelial–mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix, Bull Braz Math Soc (2016).

[2] N. Kolbe, J. Katuchova, N. Sfakianakis, N. Hellmann, M. Lukacova: A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: The urokinase model, Appl Math Comp (2015).
CGPW04 10th December 2015
14:15 to 15:00
Pasquale Ciarletta Chemo-mechanical modeling of morphogenesis in living matter
Life phenomena result from the mutual equilibrium between the living matter and the surrounding media. A network of servo-mechanisms physiologically restores the stable equilibrium between the interior matter of a living entity in the face of external perturbative agents. In particular, living cells can balance exogenous and endogenous forces using an iterative process, also known as mechano-reciprocity. Hence, not only living matter can adapt through epigenetic remodelling to the external physical cues, but it can also respond by activating gene regulatory processes, which may also drive the onset of pathologies, e.g. solid tumours. Moreover, living materials have the striking ability to change actively their micro-structural organization in order to adjust their functions to the surrounding media, developing a state of internal tension, which even persists after the removal of any external loading. This complex mechanical and biochemical interaction can finally control morp hogenesis during growth and remodelling, leading to shape instabilities characterized by a complex morphological phase diagram. In this lecture, I will introduce few mathematical s of mechanobiology and morphogenesis in living materials [1,2], with several applications concerning solid tumours [3], gastro-intestinal organogenesis [4], bacterial colonies [5] and nerve fibers [6]. [1] Ciarletta P, Ambrosi D, Maugin G A, Preziosi L. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER, 2013, 36, 23-28. [2] Ciarletta P, Preziosi L, Maugin GA. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2013, 61, 852-872; [3] Ciarletta P. Buckling instability in growing tumour spheroids. PHYSICAL REVIEW LETTERS, 2013, 110. [4] Ciarletta P., Balbi V., Kuhl, E. Pattern selection in growing tubular tissues. PHYSICAL REVIEW LETTERS, 2014, 113, 248101. [5] Giverso, C., Verani M., Ciarletta P. JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2015, 12 [6] Taffetani M., Ciarletta P, PHYSICAL REVIEW E, 2015,91
CGPW04 10th December 2015
15:30 to 16:15
Pia Domschke Mathematical modelling of cancer invasion: The role of cell adhesion variability
Co-authors: Dumitru Trucu (University of Dundee), Alf Gerisch (TU Darmstadt), Mark Chaplain (University of St Andrews)

Cancer invasion is a complex process occurring across several spatial and temporal scales, perhaps the three most important being the intracellular, cellular and tissue scales. Key biological processes occurring during invasion are the secretion of matrix degrading enzymes, cell proliferation, the loss of cell-cell adhesion on one hand and enhanced cell-matrix adhesion on the other hand, as well as active migration. The ability of cancer cells to alter or degrade the surrounding tissue enables the cancer cells to locally invade the neighbouring region. The movement of cancer cells occurs through chemotaxis as well as haptotaxis and is supported by the binding and unbinding of molecules on the cell surface to other cells and/or the extracellular matrix (ECM). The number and strength of these binding proteins define the magnitude of cell-cell and cell-matrix adhesion and are modified by the cell’s microenvironment. Hence, the movement of the cells is not only determined l ocally but depends on the neighbourhood of the cell.

We explore the spatio-temporal dynamics of a mathematical model of cancer invasion, where cell-cell and cell-matrix adhesion are accounted for through non-local interaction terms. A non-local model of cancer invasion for a single cancer cell population is extended to a structured-population model with n cancer cell sub-populations, which may mutate into each other. The change of adhesion properties during the growth of the cancer is investigated through time-dependent adhesion parameters within the cancer cell sub-populations as well as those between the cancer cells and the components of the extracellular matrix. We focus on one and two cancer cell sub-population models in two spatial dimensions, which show heterogeneous dynamics in our computational simulation results.
CGPW04 11th December 2015
09:00 to 10:00
Jose A. Carrillo Swarming Models with Repulsive-Attractive Effects: Pattern Stability
I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random data particle simulations, flocks and mills, and their qualitative behavior.
CGPW04 11th December 2015
10:00 to 11:00
Nicholas Hill Multiscale modelling of pressure and flow in the pulmonary circulation
A multiscale computational model has been developed to predict flow and pressure in the pulmonary circulation, in which the flow and pressure in the smaller blood vessels are described using linearised equations in pairs of asymmetric structured trees joined at the roots. The geometric and elastic properties of all the blood vessels are described by physiological parameters. Magnetic resonance imaging (MRI) is used to determine the geometry of the large pulmonary arteries and veins, and to measure the cardiac output from the right ventricle. The flow in the large blood vessels is solved using a Lax--Wendroff scheme, and the admittances of the structured trees provide the boundary conditions linking each large artery to its respective large vein. The model predicts flow and pressure in both the large and small vessels down to 50 microns in radius, providing important data about the local physiological environment experienced by tissues and cells.

The results of simulating various pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment of circulatory diseases within the lung. We use wave intensity analysis to study the propagation of forward and backward, compression and decompression waves in our model. The approximations for the pulse wave velocity used in experiments on wave intensity analysis are assessed, and reflected waves lower the peak pressure in the right ventricle.
CGPW04 11th December 2015
11:30 to 12:30
Alf Gerisch Nonlocal models for interaction driven cell movement
Authors: A. Gerisch, K.J. Painter, J.M. Bloomfield, J.A. Sherratt

Instructing others to move is fundamental for many populations, whether animal or cellular. Often such commands are transmitted by contact, such that an instruction is relayed directly from signaller to receiver: for cells, this can occur via receptor–ligand mediated interactions at their membranes, potentially at a distance if a cell extends long filopodia. Given that commands ranging from attractive to repelling can be transmitted over variable distances and between cells of the same (homotypic) or different (heterotypic) type, these mechanisms can clearly have a significant impact on the organisation of a tissue.   In this talk we consider nonlocal models based on integro-PDEs to model contact based cell movement. We describe some specific applications and highlight the mathematical and numerical challenges that the models present.
CGPW04 11th December 2015
13:30 to 14:15
Arik Yochelis Pattern formation by molecular motors in cellular protrusions
Co-authors: S. Ebrahim (NIH, US), B. Millis (NIH, US), R. Cui (NIH, US), B. Kachar (NIH, US), M. Naoz (Weizmann Institute of Science, Israel), N. S. Gov (Weizmann Institute of Science, Israel)

Actin-based cellular protrusions are an ubiquitous feature of cells, performing a variety of critical functions ranging from cell-cell communication to cell motility. The formation and maintenance of these protrusions relies on the transport of proteins via myosin motors, to the protrusion tip. While tip-directed motion leads to accumulation of motors (and their molecular cargo) at the protrusion tip, it is observed that motors also form rearward moving, periodic and isolated aggregates. Not only that these aggregates are apparently important to the recycling of the motors but also their origins and mechanisms are open puzzles. Motivated by novel experiments, a mass conserving nonlinear reaction-diffusion-advection model is proposed. Analysis of the model provides insights into pattern selection mechanisms, i.e., how local and global bifurcations, and boundary conditions lead to emergence of pulses and traveling waves. These pattern selection mechanisms are found not only to qualitatively agree with empirical observations but open new vistas to the transport phenomena by molecular motors in general.

CGPW04 11th December 2015
14:15 to 15:00
Christian Mazza Self-organization and pattern formation in auxin flux
The plant hormone auxin is instrumental for plant growth and morphogenesis. In the shoot apical meristem , the auxin flux is polarized through its interplay with PIN proteins. Concentration based mathematical models of the auxin flux permit to explain some aspects of phyllotaxis , where auxin accumulation points act as auxin sinks and correspond to primordia. Simulations show that these models can reproduce geometrically regular patterns like spirals in sunflowers or Fibonacci numbers. We propose a mathematical study of a related non-linear o.d.e. using Markov chain theory. We will next consider a concurrent model which is based on the so-called flux hypothesis, and show that it can explain the self-organization of plant vascular systems.

CGPW04 11th December 2015
15:30 to 16:15
Jocelyn Etienne Cells and embryos as flowing shells: analytical and numerical approaches for viscoelastic liquid shells
Actomyosin networks are known to be much denser at external surfaces of cells and early embryos than in their bulk. They are also known to be the major mechanical element allowing the cell to maintain its shape and governing its dynamics: myosin molecular motors convert biochemical energy into mechanical action, which can resolve in increased tension or deformation depending on boundary conditions [1].

Similarly, during early morphogenesis of embryos, actomyosin forms a surfacic continuum, seamed at cell-cell boundaries by so called adherens junctions, over a thikness of less than a micron at the outer surface of the 50 -micron ellipsoidal embryo. Gene expression is known to lead to successive patternings of myosin density within this actomyosin continuum, which in turn is necessary for the large morphogenetic movements of early embryogenesis to occur. However, while we know that such a myosin patternings are causal, the mechanism by which they govern the correct morphogenetic flows remains unclear. Decyphering it necessitates to resolve the mechanical balance of the embryo with the myosin force-production as a source term.

After presenting the general problem in a closed form suitable for mathematical analysis, I will present three particular cases:
- Single cells in a liquid bridge-like geometry, allowing a partial analytical resolution of the viscoelastic mechanical problem.
- Ventral furrow formation of the Drosophila embryo, for which elasticity approaches are possible at short times.
- The surface flow during germ-band extension of Drosophila, for which we have developped a new surface finite element technique allowing us to solve compressible Stokes-like problems in which velocities are tangential to a curved surface.

[1] J. Étienne, J. Fouchard, D. Mitrossilis, N. Bufi, P. Durand-Smet and A. Asnacios, 2015. Cells as liquid motors: Mechanosensitivity emerges from collective dynamics of actomyosin cortex. Proc. Natl. Acad. Sci. USA 112(9):2740–2745.