## Collective dynamics and self-organization in biological sciences

ICMS, 15 South College Street

#### 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. There will be a limited number of additional workshop spaces open for public application. To apply to attend, please complete this application form. The closing date for applications is 12 March 2018 and all applicants will be notified of decisions after that date.

### Programme

To be announced

### Participants

Pedro Aceves-Sanchez, Imperial College London

Luca Alasio, University of Oxford

Rafael Bailo, Imperial College London

Ruth Baker, University of Oxford

Arezki Boudaoud, Ecole Normale Superieure de Lyon

Maria Bruna, University of Oxford

Jose Antonio Carrillo, Imperial College London

Maria Rita D'Orsogna, CSUN

Pierre Degond, Imperial College London

Marie Doumic Jauffret, INRIA, UPMC and Wolfgang Pauli Institute

Raluca Eftimie, University of Dundee

Marina Ferreira , Imperial College London

Amic Frouvelle, Paris Dauphine

Rasa Giniunaite, University of Oxford

Arnina Goodlad, University of Dundee

Veronica Grieneisen, John Innes Center

Sophie Hecht, Imperial College London

Pierre-Emmanuel Jabin, University of Maryland

Laura Johnston, Columbia University

Alexandre Kabla, University of Cambridge

Anais Khuong, Francis Crick Institute

Anna Kicheva, IST Austria

Paul Kulesa, Stowers Institute

Hsin-Yi Lin, University of Maryland

Angelika Manhart, Courant Institute New York University

Yanlan Mao, University College London

Glenn Marion, Biomathematics & Statistics Scotland

Sara Merino-Aceituno, University of Sussex

Matthias Merkenschlager, Imperial College

Kevin Painter, Heriot-Watt University

Matthieu Perez, Imperial College London

Diane Peurichard, INRIA

Gunnar Pruessner, Imperial College London

Tertius Ralph, University of Auckland

Gergely Rost, University of Oxford

Christian Schmeiser, University of Vienna

Markus Schmidtchen, Imperial College London

Jonathan Sherratt, Heriot-Watt University

Mat Simpson, Queensland University of Technology

Brian Stramer, Kings College

Christina Surulescu, Technische Universitat Kaiserslautern

Eric Theveneau, CNRS and University Paul Sabatier

Ariane Trescases, CNRS

Kees Weijer, University of Dundee

Marie-Therese Wolfram, University of Warwick

Ewelina Zatorska, University College London

### Talks

**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 **

To be announced

**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 **

To be announced

**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

**Mao, Yanlan
**

*Tissue dynamics in development and repair *

Actomyosin contractility is a key regulator of tissue dynamics. During development, tissue dynamics, such as cell intercalations and oriented cell divisions, are critical for shaping tissues and organs. However, less is known about how tissues regulate their dynamics during tissue homeostasis and repair, to maintain their shape after development. In this talk, we will discuss how tissues respond to mechanical perturbations, such as stretching or wounding, by altering their actomyosin contractile structures, to change tissue dynamics, and thus preserve tissue shape and patterning.

**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**

To be announced

**Theveneau, Eric
**

*Collective migration of cephalic neural crest cells *

Cephalic neural crest cells are multipotent cells that undergo epithelial-mesenchymal transition and migrate collectively to colonize the head and neck of the developing embryo. The collective nature of the migration is due to a complex set of interactions between neural crest cells and between cells and their environment. We recently focused our attention how cells integrate local information in order to perform directional migration. For this workshop, I will present data about how cells balance positive and negative inputs and how they interact with other cell types they encounter in their vicinity during migration.

**Trescases, Ariane
**

To be announced

**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.

**Wolfram, Marie-Therese
**

*Mean field models for segregation *

We present two different mean-field models for interacting particle species, which are motivated by a microscopic segregation model proposed by the American economist Thomas Schelling. Schelling showed that an individual's preference to stay within its own group leads to segregation. We start with a discrete lattice model, in which transaction rates depend on the perceived average population density in the neighbourhood and the physically available space. Next we formally derive the corresponding mean-field equations, discuss their stationary states as well as their linear stability. Finally we illustrate the dynamics with numerical simulations.