skip to content
 

Timetable (CGPW02)

Cell mechanics, morphogenesis and pattern formation: perspectives from the experimental and theoretical points of view

Monday 14th September 2015 to Friday 18th September 2015

Monday 14th September 2015
09:00 to 09:40 Registration
09:40 to 09:50 Welcome from Christie Marr (INI Deputy Director)
09:50 to 10:00 Overview INI 1
10:00 to 11:00 Anne Ridley (King's College London)
Cell motility and signalling to the cytoskeleton
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Rudolf Leube (RWTH Aachen University)
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.
INI 1
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 Christian Schmeiser (Universität Wien)
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.

Related Links
INI 1
14:15 to 15:00 Andrew Goryachev (University of Edinburgh)
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.
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:00 Discussion: what do we want to learn? INI 1
16:00 to 17:00 C Elliott (University of Warwick)
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.
INI 1
17:00 to 18:00 Wine Reception
Tuesday 15th September 2015
09:00 to 10:00 Denis Wirtz (Johns Hopkins University)
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.
INI 1
10:00 to 11:00 Robert Kay (MRC Laboratory of Molecular Biology)
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.

Related Links
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Stephanie Portet (University of Manitoba)
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?
INI 1
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 Thomas Woolley (University of Oxford)
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.
INI 1
14:15 to 15:00 José Manuel García Aznar (Universidad de Zaragoza)
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
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 John Mackenzie (University of Strathclyde)
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.
INI 1
16:15 to 17:00 Michael Beil (Universität Ulm)
Cell mechanics as a target to regulate extravasation of neutrophils
INI 1
Wednesday 16th September 2015
09:00 to 10:00 Carl-Philipp Heisenberg (IST Austria)
TBA
INI 1
10:00 to 11:00 Benjie Ovryn (Albert Einstein College of Medicine)
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.
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Kees Weijer (University of Dundee); (University of Dundee)
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.

Related Links
INI 1
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 Edward Green (University of Adelaide)
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.
INI 1
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.
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 Bakhtier Vasiev (University of Liverpool)
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.
Related Links
INI 1
16:15 to 17:00 Behruz Bozorg (Lund University)
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.
INI 1
19:30 to 22:00 Conference Dinner at Cambridge Union Society hosted by Cambridge Dining Co.
Thursday 17th September 2015
09:00 to 10:00 Sean Gregory Megason (Harvard University)
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.
INI 1
10:00 to 11:00 Paul Kulesa (CALTECH (California Institute of Technology))
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.
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Kishore Mosaliganti (Harvard University)
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.
INI 1
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 Sharon Lubkin (North Carolina State University)
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.
INI 1
14:15 to 15:00 Axel Voigt (Technische Universität Dresden)
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.
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 Bjorn Stinner (University of Warwick)
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.

Related Links
INI 1
16:15 to 17:00 Xiaoyu Luo (University of Glasgow)
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.

Related Links
INI 1
Friday 18th September 2015
09:00 to 10:00 Ulrich Schwarz (Ruprecht-Karls-Universität Heidelberg)
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.

Related Links
INI 1
10:00 to 11:00 Jocelyn Etienne (CNRS (Centre national de la recherche scientifique)); (Université de Grenoble)
Rheology of actomyosin and emergent mechanical properties of cells
INI 1
11:00 to 11:30 Morning Coffee
11:30 to 12:30 Roeland Merks (Centrum voor Wiskunde en Informatica (CWI)); (Universiteit Leiden)
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.

Related Links
INI 1
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:15 Chandrasekhar Venkataraman (University of Sussex)
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.

Related Links
INI 1
14:15 to 15:00 Naomi Nakayama (University of Edinburgh)
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.

Related Links
INI 1
15:00 to 15:30 Afternoon Tea
15:30 to 16:15 John King (University of Nottingham)
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.
INI 1
16:15 to 17:00 John Dallon (Brigham Young University)
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.
INI 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons