Collective dynamics and self-organization in biological sciences

Monday 30 April to Friday 4 May 2018

ICMS, 15 South College Street, Edinburgh, EH8 9AA

Organisers

  • Ruth Baker, University of Oxford
  • Pierre Degond, Imperial College London
  • Raluca Eftimie, University of Dundee
  • Pierre-Emmanuel Jabin, University of Maryland
  • Sara Merino-Aceituno, University of Sussex

Self-organization is pervasive in biology as living organisms are by essence systems that have self-assembled and self-organized in the course of their development. Self-organization refers to the ability of systems made of a large number of independent agents interacting through rather simple and local rules to generate large scale spatio-temporal coherent structures with typical dimensions orders of magnitude larger than those associated with each individual agent.

By bringing together mathematicians and biologists, this will workshop will provide a broad overview of the various self-organization mechanisms that prevail at the various scales and the mathematical models by which they can be described or even explained. Through this interaction between experts from different disciplines, the workshop aims to make progress towards determination of the key biological mechanisms that enable self-organisation at each scale and across the scales, and towards the derivation of suitable `universal' mathematical models able to describe them across the scales.

The value of this workshop is twofold. For the biologists, it will reinforce their link with mathematicians and, by this strengthened relationship, will enlarge the range of models that they can use to probe observed biological complexity. For the mathematicians, it will broaden the repertoire of case studies with which to confront their methodologies and practice. It will suggest new systems where models are still preliminary if no existent and which may require the development of new mathematical frameworks. For the two communities, it will offer the opportunity of building trans-disciplinary teams that can easily share knowledge, models and data and apply to major research councils in UK and in Europe for large grant funding.

Topics to be covered at the workshop will include:

  • collective dynamics from the cell-scale to the population-scale (collective cell migration, flocking, etc)
  • spatio-temporal pattern formation and self-organization (cell sorting, developmental biology, tumour growth epithelial-mesenchymal transition)
  • emergent networks (vascularization, tumor angiogenesis, neural system, plant root formation, leaf venation, social insect nest structures, ant trails)
  • pattern formation in gene expression regulation, control of stochasticity, cell-fate decision-making (e.g. in the maturation of immunity cells)
  • mechanical regulation of collective dynamics (role of the congestion constraint, packing and jamming, cluster formation), particularly in cases coming from developmental biology and flocking behavior
  • data analysis and model calibration and data-model coupling.

Arrangements

Invited speakers and participants were sent an ICMS email invitation in late November.

PUBLIC APPLICATION
The closing date for applications has passed and all applicants have been notified.

Programme

Monday 30th April 2018

08:45-09:30

Registration & coffee/tea in the Chapterhouse, Level 1

09:30-09:40

Welcome

Chair: Degond, Pierre (Imperial College London)

09:40-10:20

Weijer, Kees (University of Dundee)
Cellular behaviours underlying tissue dynamics during primitive streak
formation in the chick embryo

10:20-11:00

Stramer, Brian (Kings College)
Cell steering through persistent and global action flow

11:00-11:30

Coffee/tea in the Chapterhouse, Level 1

Chair: Surulescu, Cristina (Technische Universitat Kaiserslautern)

11:30-12:10

Frouvelle, Amic (Paris Dauphine)
Stability of dirac masses for simple alignment processes

12:10-13:40

Lunch in the Chapterhouse, Level 1

Chair: Frouvelle, Amic (Paris Dauphine)

13:40-14:20

Simpson, Mat (Queensland University of Technology)
Mathematical models for cell migration with real-time cell cycle dynamics

14:20-15:40

Discussion group

15:40-16:10

Coffee/tea in the Chapterhouse, Level 1

Chair: Painter, Kevin (Heriot-Watt University)

16:10-16:50

Manhart, Angelika (Courant Institute, New York University)
Traveling waves in myxobacteria

16:50-18:00

Poster session/informal wine reception in Chapterhouse, Level 1

 

Tuesday 1st May 2018

Chair: Baker, Ruth (University of Oxford)

09:00-09:40

Doumic Jauffret, Marie (INRIA, UPMC & Wolfgang Pauli Institute)
Estimating the division in growing and dividing populations

09:40-10:20

Kabla, Alexandre (University of Cambridge)
Mechanics of cellularised tissues

10:20-10:50

Coffee/tea in the Chapterhouse, Level 1

Chair: Doumic Jauffret, Marie (INRIA, UPMC & Wolfgang Pauli Institute)

10:50-11:30

Bruna, Maria (University of Oxford)
Reactions, diffusion and volume exclusion in a heterogeneous system
of interacting particles

11:30-12:10

Kulesa, Paul (Stowers Institute, Kansas)
Collective migration of the embryonic neural crest

12:10-12:15

Group photograph at front entrance

12:15-13:40

Lunch in the Chapterhouse, Level 1

Chair: Weijer, Kees (University of Dundee)

13:40-14:20

Surulescu, Christina (Technische Universitat Kaiserslautern)
Model classes for cancer cell migration: the influence of the tumour
microenvironment

14:20-15:40

Discussion group

15:40-16:10

Coffee/tea in the Chapterhouse, Level 1

Chair: Manhart, Angelika (Courant Institute, New York University)

16:10-16:50

Theveneau, Eric (CNRS & University Paul Sabatier)
Exploring the dynamics of pseudostratified epithelia using agent-based
computational modelling

16:50-17:30

Ariel, Gil (Bar Ilan University)
Chaos and Levy walks in swarming bacteria

17:30

Doors open for public lecture

18:00-19:00

Public lecture by Pierre Degond: Mathematics of the Mob

19:00-20:00

Informal wine reception in Chapterhouse, Level 1

 

Wednesday 2nd May 2018

Chair: Merino-Aceituno, Sara (University of Sussex)

09:00-09:40

Carrillo, Jose Antonio (Imperial College London)
Swarming models with local alignment effects: phase transition and hydrodynamics

09:40-10:20

Merkenschlager, Matthias (Imperial College London)
Self-organisation and the function of the genome

10:20-10:50

Coffee/tea in the Chapterhouse, Level 1

Chair: Carrillo, Jose Antonio (Imperial College London)

10:50-11:30

Trescases, Ariane (CNRS, Institut de Mathematiques de Toulouse)
Quaternions in collective dynamics

11:30-12:10

D’Orsogna, Maria Rita (California State University at Northridge)
Three dimensional swarming in viscous fluids

12:10 onwards

Free afternoon

 

Thursday 3rd May 2018

Chair: Eftimie, Raluca (University of Dundee)

09:00-09:40

Peurichard, Diane (INRIA)
Modelling of dynamical networks: from micro- to macro- descriptions

09:40-10:20

Boudaoud, Arezki (Ecole Normale Superieure de Lyon)
Stochasticity and robustness in plant morphogenesis

10:20-10:50

Coffee/tea in the Chapterhouse, Level 1

Chair: D’Orsogna, Maria Rita (California State University at Northridge)

10:50-11:30

Kicheva, Anna (IST Klosterneuburg)
Coordination of progenitor specification and growth in the developing spinal cord

11:30-12:10

Sherratt, Jonathan (Heriot-Watt University)
Self organisation in arid vegetation

12:10-13:40

Lunch in the Chapterhouse, Level 1

Chair: Boudaoud, Arezki (Ecole Normale Superieure de Lyon)

13:40-14:20

Johnston, Laura (Columbia University)
Tissue ecology: sensing and responding to differences in cellular fitness during growth

14:20-15:40

Discussion group

15:40-16:10

Coffee/tea in the Chapterhouse, Level 1

Chair: Kicheva, Anna (IST Klosterneuburg)

16:10-16:50

Grieneisen, Veronica (John Innes Centre, Norwich)
Self-organisation of the cell’s compass, collective coordination in plant and animal tissues, and emerging traffic-jams

16:50-17:30

Tozluoglu, Melda (University College London)
Mechanical Regulation of Tissue Growth and Shape Formation

17:30-18:30

Poster session in the Chapterhouse, Level 1

19:00-22:00

Workshop dinner at Blonde Restaurant, St Leonard's Street, Edinburgh (see map)

 

Friday 4th May 2018

Chair: Jabin, Pierre-Emmanuel (University of Maryland)

09:00-09:40

Painter, Kevin (Heriot-Watt University)
Modelling cell movement: from tissue organisation to disease

09:40-10:20

Schmeiser, Christian (University of Vienna)
A kinetic model with local interactions for myxobacteria colonies

10:20-10:50

Coffee break in the Chapterhouse, Level 1

10:50-11:20

Discussion group reports

11:20-12:00

Final discussions

12:00

Close of workshop

  

Talks

Ariel, Gil
Chaos and Levy walks in swarming bacteria
Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces. Swarming is typically characterized by densely packed groups moving in coherent patterns of whirls and flows. Recent experiments showed that within such dense swarms, bacteria are performing super-diffusion that is consistent with a Levy walk. We present a simple model suggesting that chaos and Levy walking are a consequence of group dynamics. Mathematically, the model presents a new mechanism for Levy walks in chaotic maps that are not volume preserving. Biologically, it explains how cells can fine-tune the geometric properties of their trajectories. Joint work with Avraham Be'er (BGU) and Andy Reynolds (Rothamsted Research, UK).

Boudaoud, Arezki
Stochasticity and robustness in plant morphogenesis
How do organisms cope with cellular variability to achieve well-defined morphologies and architectures? We are addressing this question by combining experiments with live plants and analyses of (stochastic) models that integrate cell-cell communication and tissue mechanics. During the talk, I will survey our results concerning plant architecture (phyllotaxis) and organ morphogenesis.

Bruna, Maria
Reactions, diffusion and volume exclusion in a heterogeneous system of interacting particles
Cellular migration can be affected by short-range interactions between cells such as volume exclusion, long-range forces such as chemotaxis, or reactions such as phenotypic switching. In this talk I will discuss how to incorporate these processes into a discrete or continuum modelling frameworks. In particular, we consider a system with two types of diffusing hard spheres that can react (switch type) upon colliding. We use the method of matched asymptotic expansions to obtain a systematic model reduction, consisting of a nonlinear reaction-diffusion system of equations. Finally, we demonstrate how this approach can be used to study the effects of excluded volume on cellular chemotaxis.

Carrillo, Jose Antonio
Swarming models with local alignment effects: phase transition & hydrodynamics
Phase transitions for a local Cucker-Smale model will be discussed in connection to the Vicsek model. Hydrodynamics are obtained by scaling limits by penalization of the asymptotic velocity term.

D'Orsogna, Maria Rita
Three dimensional swarming in viscous fluids
We introduce a three-dimensional theory for self-propelled particle swarming in a viscous fluid. Fluid opacity, mechanism of self-propulsion, and type of particle-particle interaction all affect emergent collective behaviour. In “clear fluids” swimmers have full knowledge of their surroundings and can adjust their velocities with respect to the lab frame, while in “opaque fluids” they control their velocities only in relation to the local fluid flow. We also distinguish “social” interactions that affect only a particle’s propensity to swim towards or away from neighbours from direct “physical” interactions. The latter can be short-ranged but can lead to longer-ranged fluid-mediated hydrodynamic forces, effectively amplifying the range over which particles interact. Finally, we model both “pusher” and “puller” particles, depending on how they interact with the fluid as they swim through it. In addition to canonical mills and flocks, we discover a number of new collective three-dimensional patterns including flocks with prolate or oblate shapes, recirculating pelotonlike structures, and jetlike fluid flows that entrain particles mediating their escape from the centre of mill-like structures.

Doumic Jauffret, Marie
Estimating the division in growing and dividing populations
Growing and dividing populations may be described either by stochastic branching processes or by integro-differential equations, both related by the fact that the integro-differential equation may be seen as the Kolmogorov equation of the branching process. Denoting $u(t,x)$ the concentration of individuals of size $x$ at time $t,$ a typical growth-fragmentation equation may be written as $$frac{partial}{partial t} u(t,x) + frac{partial}{partial t} (g(x) u(t,x) ) + B(x) u(t,x) =intlimits_0^1 B(frac{x}{z}) u(t,frac{x}{z}) frac{dk_0 (z)}{z},$$ where $g(x)$ is the growth rate, $B(x)$ the division rate, and $k_0$ is called the (self-similar) fragmentation kernel, which characterizes the probability for a dividing particle of size $frac{x}{z}$ to give rise to an offspring of size $x$. During the last decade, using the asymptotic behaviour of this equation or of the related stochastic process to estimate the division rate ($B(x)$ in the equation) of a population has led to many interesting questions and results, in mathematics as well as in biology. In this talk, I will review some of them, and focus on the question of estimating the fragmentation kernel $k_0$, which revealed a much more ill-posed problem than estimating the division rate $B(x)$. This is joint work with Magali Tournus, Miguel Escobedo and Wei-Feng Xue.

Frouvelle, Amic
Stability of Dirac masses for simple alignment processes
We study the long-time behaviour of simple kinetic alignment processes on the sphere. Due to the lack of conservation of the center of mass (which is not even well-defined), we do not know in advance where the probability density function is going to concentrate. However, we are able to show that it will actually converge to a Dirac mass, and to provide the rate of convergence.

Grieneisen, Veronica
Self-organization of the cell's compass, collective coordination in plant and animal tissues, and emerging traffic-jams
I will show how we can view animal and plant cell polarity as being governed by simple biochemical processes, which generate a plethora of diverse patterning properties. Through a simple mathematical method – Local Perturbation Analysis – we can map polarity behaviours to different kinetic parameters. Importantly, core ability of a cell to polarize in isolation from others, leads to the collective emergence of tissue polarity, dependent on the different mode of cell-cell interaction. Finally, we will adopt a morphoengineering view on plant-nutrient uptake, which reveals hidden dynamical constraints that operate in all transport system of polarized tissues, to avoid traffic-jam behaviour.

Johnston, Laura
Tissue Ecology: Sensing and Responding to Differences in Cellular Fitness During Growth
Cells in developing tissues and organs have evolved mechanisms to promote cooperative interactions with their neighbors, and uncooperative cells are eliminated from the tissue by a dynamic process called cell competition. Cell competition allows proliferating cells to adapt to changes in their environment and promotes optimal animal fitness. Our work in Drosophila identified a signaling module, mediated by a cohort of immune response components including Toll receptors, its secreted ligand, Spätzle (Spz), and NF-kappaB factors, that recognizes sub-par cells in growing organs and competitively eliminates them via apoptosis. However, this mechanism can be exploited by “cheater” cells to expand their territory, as occurs in cancer. Notably, clonal expression of Myc leads cells to rapidly acquire super-competitor status, allowing them to send a killing signal to their wild-type neighbors and promote their own growth. I will discuss the results of our investigation into how signal activation is controlled during Myc super-competition. Although Spz circulates in the larval hemolymph and is readily activated upon pathogenic infection, our results indicate that for cell competition, the activation of Spz by specific serine proteases (SPs) is strictly confined to the imaginal disc, as is the Spz-mediated killing signal. This geographical constraint allows errors in tissue fitness to be corrected without compromising organismal physiology. More generally, our results lead us to propose a model of fitness surveillance in developing tissues, whereby fitness is continually assessed by the expression of Spz and its activating SPs, yielding a potentially dangerous killing signal. Cells not healthy enough to tolerate this signal are outcompeted by the signaling cells. “Cheaters” that over-produce the signal are only able to compete with other cells if fit enough to tolerate it themselves. We speculate that such an inherent link between cellular fitness and the capacity to produce and respond to competitive signals may underlies numerous modes of cell competition.

Kabla, Alexandre
Mechanics of cellularised tissues
Cellularised materials are composed of cells interfaced through specialised junctions that link the cytoskeleton of one cell to that of its neighbours, allowing for the generation and transmission of forces. Cellularised materials are common in early development and adult tissues where they can be found in the form of cell sheets, cysts, or amorphous aggregates and in pathophysiological conditions such as cancerous tumours. Given the growing realisation that forces can regulate cell physiology and developmental processes, understanding how cellularised materials deform under mechanical stress or dissipate stress appear as key biological questions. This talk will present a number of experimental and numerical techniques developed to bridge cell dynamics and tissue rheology, and identify some of the biological processes controlling the mechanical response of simple tissues.

Kicheva, Anna
Coordination of progenitor specification and growth in the developing spinal cord
As the spinal cord grows during embryonic development, an elaborate pattern of molecularly distinct neuronal precursor cells forms along the DV axis. This pattern depends both on the dynamics of a morphogen-regulated gene regulatory network, and on tissue growth. We study how these processes are coordinated. Our data revealed that during mouse and chick development the gene expression pattern changes but does not scale with the overall tissue size. These changes in the pattern are sequentially controlled by distinct mechanisms. Initially, neural progenitors integrate signaling from opposing morphogen gradients to determine their identity by using a mechanism equivalent to maximum likelihood decoding. This strategy allows accurate assignment of position along the patterning axis and can account for the observed precision and shifts of pattern. During the subsequent developmental phase, cell-type specific regulation of differentiation rate, but not proliferation, elaborates the pattern.

Kulesa, Paul
Collective migration of the embryonic neural crest
Embryonic cells often travel long distances to help build organs, yet our understanding of how cells respond to dynamic tissue growth and molecular signals to self-organize into collective groups is not fully understood. The highly invasive neural crest is an excellent model to study mechanisms of collective cell migration since cells are accessible to imaging, physical and molecular manipulation. We have developed a dynamic in vivo imaging platform in avian embryos that permits single cell interrogation of cell behaviors and changes in gene expression. We have made two recent exciting discoveries. First, we learned that the mesoderm and extracellular matrix through which neural crest cells travel is growing in a heterogeneous manner during head morphogenesis. Second, we found there is molecular heterogeneity within a neural crest cell migratory stream that includes a consistent transcriptional signature within cells at the invasive front. I will discuss these recent experimental discoveries and the integration of empirical data into a computational model of neural crest cell migration we have developed through collaboration. Our long term goal is to better understand the fundamental mechanisms that underlie collective cell migration as a model in human development and cancer.

Manhart, Angelika
Traveling waves in myxobacteria
Myxobacteria are social bacteria, that can glide in 2D and frequently reverse their direction. They can form both aggregates and counter-propagating, interacting waves. In this talk I will present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on microscopic interaction rules that can be formulated as a particle-based model and set within the SOH (Self-Organized Hydrodynamics) framework. The strength of this combined approach is that microscopic information can be incorporated into the particle model in a straight-forward manner, whilst the continuous model can be analyzed using mathematical tools, such as stability and asymptotic analysis. It has been suggested that bacteria are not able to react to signals immediately after they have reversed their direction. Our analysis reveals that this insensitivity period is not necessary for wave formation, but essential to wave synchronization. A second focus will be the existence and stability of such traveling waves moving in two opposing waves frames. Fascinatingly, while the wave profiles are unchanged, the wave composition changes and the fractions of reversible and non-reversible bacteria form waves traveling in the opposite direction. I will discuss the explicit construction of such waves and show simulation results. Joint work with Pierre Degond and Hui Yu

Merkenschlager, Matthias
Self-organisation and the function of the genome
Mammalian genomes comprise billions of nucleotides, or several meters of linear DNA. To fit into cell nuclei that measure a few microns across, genomic DNA is packaged into chromatin, the building material of chromosomes. The organisation of chromatin in the nucleus is non-random, and driven by at least two, partially antagonistic principles. One is the segregation of active from repressive chromatin states, which has features of self-organisation. The segregation of active from repressive chromatin states is counteracted by genome organiser proteins such as cohesin and CTCF. Cohesin and CTCF form self-interacting domains of chromatin that can contain mixed chromatin states. We have removed genome organiser proteins to explore the consequences of this mixing on gene expression, one of the key functions of the genome. Deletion of cohesin and CTCF affects the function of specific subsets of genes, namely genes that are expressed in an inducible fashion. We are testing the idea that inducibility requires the mixing of chromatin states.

Painter, Kevin
Modelling cell movement: from tissue organisation to disease
Cells and organisms move and position themselves according to various environmental cues, ranging from short range adhesive and repulsive interactions to long range guided responses due to factors such as chemicals. In this talk I will describe the modelling of these fundamental processes from both individual and continuous scale, and discuss their application in areas including developmental biology and cancer invasion. Along the way I will discuss the numerous modelling, numerical and analytical challenges posed.

Peurichard, Diane
Modelling of dynamical networks: from micro- to macro- descriptions
In this talk we study the derivation of kinetic and macroscopic models (PDE) from agent-based models for complex dynamical networks of interconnected particles. The agent-based model features particles (2D spheres) having the ability to link/unlink with its close neighbours by creating springs of given equilibrium length. In the limit of large number of particles, we formally obtain a kinetic system of two equations: one for the distribution function of individual particles and one describing the pairs of linked particles. In the large-scale limit and under scaling assumptions, we obtain an aggregation diffusion equation which numerically match the limiting behaviour of the particle model. The linear and non-linear stability analysis of the homogeneous states of the macroscopic model enable to identify precise criteria linking the aggregative capacity of the model to few key model parameters. This model is then extended to the two-species case and enable the study of cell segregation and border sharpening in biological systems.

Schmeiser, Christian
A kinetic model with local interactions for myxobacteria colonies
The derivation and first analytical and numerical results for a Boltzmann like kinetic model for myxobacteria colonies on flat substrates is presented. The model is two-dimensional and features constant speeds between collisions as well as alignment and reversal interactions.

Sherratt, Jonathan
Self organisation in arid vegetation
I will discuss the use of mathematical modelling to study the formation of vegetation patterns in arid regions. I will focus on the prediction of history dependence in pattern wavelength, which has important implications for the understanding of the future of semi-arid vegetation in the context of a changing climate. A detailed understanding of pattern hysteresis involves the calculation of pattern stability, and I will explain a new approach to this using numerical continuation, which has important implications for pattern formation in a number of other biological contexts.

Simpson, Mat
Mathematical models for cell migration with real-time cell cycle dynamics
The fluorescent ubiquitination-based cell cycle indicator, known as FUCCI, enables the visualisation of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present new mathematical models which can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of travelling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed. We conclude by outlining future directions of our work in this area.

Stramer, Brian
Cell steering through persistent and global actin flow
Here we exploit Drosophila embryonic macrophages to investigate the control of actin dynamics during cell migration. Correlation of global actin flows with cell migration reveals that, unlike leading edge activity, the actin flow behind the leading edge is persistent and highly polarized in randomly migrating cells. To determine whether directed migration is controlled in a similar fashion we examined the chemotaxis of macrophages migrating towards wounds. Wounding led to a dramatic increase in leading edge directional persistence, which matched the directional persistence of the actin flow. These data suggest that the leading edge is specifically controlling directed cell migration while the inherent persistence of randomly migrating cells is regulated by the global organization of the actin retrograde flow. To further understand the mechanisms regulating actin flow organization we examined the role of Myosin contraction and Cofilin mediated actin-network severing. Indeed, not only was the rate of retrograde flow reduced in myosin and cofilin mutant macrophages, the global organization of the flow was also severely affected; while control macrophages have dominant and highly persistent regions of network compression that organize the overall flow field, mutants show disorganized retrograde flow that lacks coherent organization. These data suggest that global organization of actin retrograde flow is an emergent behaviour driven by coordinated destruction/contraction of the actin network.

Surulescu, Christina
Model classes for cancer cell migration: the influence of the tumor microenvironment
We present several model classes for cancer invasion, thereby paying attention to the influence of soluble and unsoluble components of the microenvironment on the tumor spread. Various modeling scales are accounted for, and the settings couple different types of PDEs.

Theveneau, Eric
Exploring the dynamics of pseudostratified epithelia using agent-based computational modelling
Pseudostratified epithelia are a special type of columnar epithelia in which cells are thin and elongated. Nuclei packing is very high and forces nuclei to distribute along the apicobasal axis creating multiple layers of nuclei within a monolayer of cells. These epithelia are very common, they are found during development (e.g placodes, central nervous system, drosophila imaginal discs) and in adults (e.g trachea, epididimys). One interesting characteristics of pseudostratified epithelia is the coordinated movements of nuclei during the cell cycle called interkinetic nuclear migration (IKNM). IKNM is regulated by actomyosin and microtubules and as such is difficult to specifically impair without affecting other cell activities such as mitosis, cell adhesion and apicobasal polarity. Because of these technical limitations, the specific impact of IKNM on the development of pseudostratified epitehlia has remained largely unexplored. To overcome this issue, we developed a 2D ag ent-base d model recapitulating the dynamics of pseudostratified epithelia, including IKNM, using the developing chicken neural tube as a pseudoepithelium of reference. Each cell is modelled as a nucleus connected to a set of springs modelling the viscoelastic properties of the cytoplasm/cytoskeleton and cell adhesion. Cell proliferation is implemented according to known duration of cell cycle phases measured in vivo. Characteristics of the springs linked to the nucleus change during the cell cycle to model the pre-mitotic rapid apical migration (PRAM) characteristics of IKNM. Using the model, we have explored the links between growth, pseudostratification, cell and tissue shapes and IKNM. Our results shed a new light on the roles of IKNM during the growth of pseudostratified epithelia.
Joint work with M. Ferreira, F. Duarte, P. Degond.

Tozluoglu, Melda
Mechanical Regulation of Tissue Growth and Shape Formation
Understanding the regulation of tissue growth is of significant clinical interest, and can shed light on processes ranging from tissue regeneration to inhibition of uncontrolled growth in cancer. Although the roles of biochemical regulatory mechanisms of tissue growth and shape have been key subjects of research, our understanding of the roles for mechanical properties of tissues is still limited. This imbalance stems from the difficulties in investigating mechanical roles of proteins, such as in generating tension, independently from their biochemical functions in experiments. In our computational approach, we utilise a finite element methodology to answer how the interplay between the growth rates, physical properties, and shape dynamics of cells lead to the final tissue architecture. The model system we use is the wing imaginal disc of Drosophila Melanogaster. Starting from heterogeneities in growth and physical properties, we try to identify the minimum set of requirements that drives the three-dimensional folded structure of the wing disc. Forces accumulate in the tissue due to differential growth, and we investigate the affects these forces have on the progress of shape formation.  We identify that the early growth rates of the tissue are the main driver for the specific locations of the initiated folds. In turn, stiffness differences between structurally different layers of the cells, and the restriction of the extracellular matrix  (ECM) on the growing tissue drive the fold initiation. These physical property heterogeneities and confinement effects influence fold positions to a lesser degree. Currently, we investigate the requirements for further progress of the initiated tissue folds, with a focus on required local and temporal physical property changes.

Trescases, Ariane
Quaternions in collective dynamics
We present a model for multi-agent dynamics based on rigid alignment. Each agent is described by its position and body attitude: each agent travels at a constant speed while trying to coordinate its solid orientation with the solid orientation of the neighboring agents. The body orientations are represented by unitary quaternions. We first introduce an individual based model in the spirit of the Vicsek model, enhanced with the body orientation dynamics. We then derive the corresponding kinetic model. From there we compute the hydrodynamical limit, leading to a self-organized hydrodynamical system based on quaternions. This is a joint work with Pierre Degond, Amic Frouvelle and Sara Merino-Aceituno.

Weijer, Kees
Cellular behaviours underlying tissue dynamics during primitive streak formation in the chick embryo
Gastrulation involves embryo wide tissue reorganizations and deformations driven by coordinated cell shape changes and rearrangements. Using a dedicated lightsheet microscope we are able to follow over 200.000 cells in the early embryo. 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. These forces are generated by local cell shape changes and cell rearrangements of mesendoderm cells. These cell rearrangements are mediated by sequential, directional contraction of aligned apical junctions in neighbouring cells. These processes are driven contraction of apical acto-myosin II cables. We will discuss our attempts to analyse and model how these cell shape changes and intercalations can self-organise on the tissue scale to result in the formation of the primitive streak.