Mathematical Methods for the Study of Self-organization in the Biological Sciences

10th-11th December 2020
online event


The actual thematic program 'Mathematical Methods for the Study of Self-Organization in the Biological Sciences' has been postponed to the 14th November - 9th of December 2022 and will take place at the Erwin Schrödinger Institute in Vienna, Austria.

As a warm-up we present a series of online talks pairing-up a mathematician/theoretician and a biologists/experimentalist that work together. Each one gives approximately half an hour talk. This event will take place on the 10-11th of December 2020. The event will also be hosted by the Erwin Schrödinger Institute, Vienna.

To participate in this event registration is compulsory (via this webpage: please go to 'Registration' and click 'new registration'). The event will be held via the Zoom platform.

Confirmed pairs of speakers

Pair 1
Pair 2
Pair 3
Pair 4
Pair 5
Pair 6


All times are Austrian times (GMT+1)
Abstracts and titles will come soon.

Thursday 10th of December

09:20-09:30 Introduction
09:30-10:30 Talk: Laurent Blanchoin & Angelika Manhart
11:00-12:00 Talk: Human Rezaei & Mathieu Mezache

14:00-15:00 Talk: Osvaldo Chara & Diane Peurichard
15:30-16:30 Talk: Gantas Perez-Mockus & Sophie Hecht

Friday 11th of December

09:30-10:30 Talk: Wei-Feng Xue & Magali Tournus
11:00-12:00 Talk: Eric Theveneau & Marina A. Ferreira

Titles and abstracts (by order of the talks)

Experimental and modelling study of the dynamic steady state of actin networks. (Angelika Manhart and Laurent Blanchoin)
The dynamic assembly and turnover of actin networks in cells control shape changes, migration and organelle function, as well as communication with extracellular substrates or neighbors. The intracellular actin cytoskeleton forms such complex intricate networks in cells that it is difficult to identify the principles of their dynamic self-organization. We have developed reconstituted systems in vitro as simplified models for the study of the cytoskeleton. We use a high-resolution surface structuration assay combined with mathematical modelling to describe the length dependence of a dynamic reconstituted actin network. We found that the length of the network is controlled by its porosity and the ADF/cofilin-actin ratio. Based on our mathematical model, we could explain how the steady state length of branched actin network emerges from the complex interplay between its biochemical, structural and mechanical properties.
Coexistence of multiple prion conformation leads to a catalytical conformational exchange (Human Rezaei)
The prion pathology is based on autonomous structural information propagation towards single or multiple protein conformational changes. Since this last decade the prion concept referring to the transmission of structural information has been extended to several regulation systems and pathologies including Alzheimer and Parkinson’s diseases. The unified theory in Prion replication implies structural information transference (SIT) from the prion to a non-prion conformer through a mechanism also called improperly, with regards to biophysical considerations “seeding” phenomenon. Recently we reported that prion replication is intrinsically source of structural diversification. The coexistence of multiple of prion assemblies with different structural and replication propensity questions how they are maintained within the same media and how they escape to best replicator selection.
The analysis of the quaternary structure dynamic of prion assemblies by light scattering, and differential scanning calorimetry revealed the existence of an exchange process within the structurally diverse prion assemblies. This exchange process has for consequence the apparition of dumped-oscillation. Data assimilation and kinetical modelling conduced us to propose a kinetical scheme in which structurally diverse prion assemblies catalytically exchange material. According to this kinetic scheme a catalytical depolymerization competes with a catalytic conformational change.
Modeling of the oscillating polymerization/depolymerization process of Prions (Mathieu Mezache)
The process of protein aggregation and fragmentation is linked to the contraction and development of a broad class of incurable neurodegenerative diseases: amyloid diseases. More especially, oscillatory kinetic phenomena are identified during the experiments on Prions diseases. We introduce a kinetic model capable of generating oscillations. The model is a variant of the polymerization/depolymerization system and considers twomonomer species: a pathological monomer that polymerizes and a monomer healthy that depolymerizes. Unlike seminal models, the depolymerization is catalytic and non-linear and a phenomenon of exchange operates between the two species of monomers and polymers. The model couples a Lotka-Volterra system for monomers to a system of growth/fragmentation: Becker-Döring in the discrete size case, Lifshitz-Slyozov in the continuous case.
Spatiotemporal distribution of cell proliferation rules the regenerative response in axolotl spinal cord (Osvaldo Chara)
Axolotls can fully regenerate spinal cord after amputation, but the underlying mechanisms are still unclear. We previously found that tail amputation triggers the reactivation of a developmental-like program in spinal cord ependymal cells (Rodrigo Albors et al., 2015. eLife. 4:e10230). We also determined a high-proliferation zone that expands and moves posteriorly over time and demonstrated that cell cycle acceleration, due to shortening of G1 and S cell cycle phases, is the major driver of regenerative growth (Rost et al., 2016. eLife. 5:e20357). What organizes cell proliferation in space and time remains unknown. In this talk, we present some results obtained from a very simple 1-dimensional stochastic mathematical model, assuming a signal initiated at the amputation plane that propagates over the spinal cord tissue with constant velocity, recruiting the ependymal cells. We also assumed that the coordinates along the cell cycle of the recruited cells are irreversibly transformed, depending on the cell cycle phase in which the cells are. Finally, we will see that the spatiotemporal distribution of cells in G1/G0 and S/G2 predicted from the model are in qualitative agreement with the experimental data gathered in a FUCCI axolotl, a transgenic axolotl that reports cell cycle status fluorescently in vivo.
A 2D hybrid agent-based/continuum model for the regeneration of axolotl spinal cord (Diane Peurichard)
Based on the simple 1D model that was shown in the previous talk, we aim to extend the model in 2D to provide a more realistic model for axolotl spinal cord regeneration. To that aim, in this talk we introduce a 2D hybrid agent-based/continuum model coupling cell dynamics, cell proliferation and injury signalling chemical flow during tissue repair. Tissue cells are modelled as non-overlapping 2D spheres which divide randomly with space-dependent proliferation rates. We suppose that cell proliferation rates depend on the local concentration of injury signalling chemicals, continuously produced at the boundary of the tissue after injury/amputation. These chemicals diffuse in the tissue and degrade at a given rate, accelerating the division of tissue cells which are in contact. We show that this simple model is able to reproduce the tissue outgrowth measured experimentally in axolotl, and we numerically analyze the influence of the chemical signal parameters on the tissue outgrowth dynamics. The model suggests that the proliferative response in axolotl spinal cord regeneration could be mainly controlled by a chemical signal spreading in the tissue after injury, and provides new insights on the signal dynamics that may be responsible for successful spinal cord regeneration.
Mechanical constraints to cell cycle progression in a pseudostratified epithelium (Gantas Perez-Mockus & Sophie Hecht)
Mechanical feedback has been proposed to constraint growth in developing epithelia. So far, much of the attention has been focused on the role of adherens junctions as mechanical sensors. Here we consider the possible role of mechanical influences that operate throughout the epithelial volume. This is particularly relevant in pseudostratified epithelia, where nuclei must migrate to the apical surface in order to proceed through mitosis. We explore how the mechanical constraints imposed by nuclear crowding and space confinement affect interkinetic nuclear migration and hence cell cycle progression. We first catalogue the 3D position, crowding index and cell cycle position for thousands of nuclei in fixed wing imaginal discs at different developmental stages. We use these data to devise an individual-based model that treats nuclei as deformable objects constrained by their cell membrane and the presence of other nuclei. In this model, the duration of G1 and S phase are imposed whereas the duration of the G2 phase is a read-out of the model. Our simulations recapitulate the increased crowding and number of nuclear layers observed in fixed tissues, and show how increase crowding impedes apical-ward movement, forcing nuclei more time in G2 before they can reach the apical surface for mitosis. The simulations also predicts that an active downward movement in G1 is required to reproduce the apical/basal distribution of nuclei in this phase, a prediction that we validate experimentally. Finally, we explore the necessity of a basal signal required for S phase entry, to account for the observed reduction of the G1 phase duration. Thus, while the crowding increases only the nuclei that are able to migrate to the basal region and back to the apical surface would be able to complete the cell cycle. Our two-gate model of cell cycle progression could account for the progressive slowing down of growth and the finite thickness of pseudostratified epithelia.
Experimental analysis of the division of amyloid fibrils (Wei-Feng Xue)
The division of amyloid protein fibrils is required for the propagation of the amyloid state, and is an important contributor to their stability, pathogenicity and normal function. Here, I will present our experimental work on resolving amyloid division and biological impact of their size distributions. By applying new theoretical results emerging from collaboration with mathematicians (detailed by Magali Tournus), these experiments to profile the dynamical stability towards breakage for different amyloid types using AFM imaging reveal particular differences in the division properties of disease- and non-disease related amyloid. Here, the disease associated amyloid formed from alpha-synuclein show lowered intrinsic stability towards breakage and increased likelihood of shedding smaller particles compared with non-disease related amyloid models. Our results enable the comparison of protein filaments’ intrinsic dynamic stabilities, which are key to unravelling their toxic and infectious potentials.
How to recover the fragmentation rate and kernel characterizing a size-structured population undergoing fragmentation? (Magali Tournus)
We address the question of estimating the fragmentation parameters – i.e. the division rate B(x) and the fragmentation kernel k(y,x) – from measurements of the size distribution f(t,.) at various times. This is a natural question for any application where the sizes of the particles are measured experimentally whereas the fragmentation rates are unknown.
The application that drives our work is the study of mechanical properties of amyloid fibrils that undergo fragmentation (are the mechanical properties related to toxicity?) and will be detailed by Wei-Feng Xue.
In this talk, I will explain why the inverse problem is well posed under reasonable assumptions, and I will focus on how we can recover the fragmentation rate and kernel.
Challenging epithelial stability (Eric Theveneau)
Epithelia are a special type of cell arrangement in which cells are tightly attached to one another. During embryo development cells can aggregate as epithelia and disperse as a mesenchyme, a collection of motile and loosely connected cells. This occurs multiple types to form the organs. These processes of dispersion and aggregation known as epithelial-mesenchymal and mesenchymal-epithelial transitions (EMT, MET) are extremely complex. They involve qualitative and quantitative changes in cell-cell and cell-matrix adhesion, cell polarity and remodeling of extracellular matrix. The paths leading to EMT have been thoroughly studied experimentally. One striking observation is that there is a wide diversity of strategies to toggle between epithelial and mesenchymal phenotypes even within a given cell population. The impact of this cell heterogeneity on the dynamic of the process is not understood. We do not know whether cells with different strategies compete or cooperate. We do not know whether a given path to EMT affects the migratory behavior of cells once they have left an epithelium. Answering these questions is important if we want to better understand the driving forces of morphogenesis during embryo development. But also, if we want to better understand how EMT might affect a tissue when it occurs as part of a disease. Indeed, in carcinoma (cancer of epithelial tissues), EMT leads to dispersion of cells and promotes stemness, migration and eventually secondary metastasis. In the lab, we use the neural tube of the chicken embryo as model of a growing epithelia that produces mesenchymal cells by EMT during embryo development. In my presentation, I will present the main principles of EMT, the experimental model, the questions we would like to address, the techniques and strategies that can be used and more importantly what currently cannot be done that led us to develop a computational strategy to substantiate our experimental work.
Modelling a packed cell tissue (Marina A. Ferreira)
In pseudostratified epithelial tissues, cells are tightly packed with almost no intercellular space. The force each cell exerts on its neighbours plays an important role in the dynamics and shape of the tissue. However the precise effect of these contact forces is not well understood, nor easily studied in the lab. To study this system, we propose a modelling framework consisting of a geometric representation of a cell which interacts with other cells through springs and non-overlapping constraints, aiming at minimizing a potential energy. Mathematically, this can be formulated as a nonconvex constrained minimization problem with a time-dependent minimizing function. Our numerical implementation consists on a time-stepping scheme involving the damped Arrow-Hurwicz algorithm for nonconvex problems. The model is validated against in vivo data taken from the chick neuroepithelium. In silico experiments show how interkinetic nuclear movements influence cell distribution and shape of the tissue over time. Our results also suggest that apicobasal elongation is not completely explained by the mechanics of the tissue, but rather requires a specific elongation program.

About the organisers

Prof Pierre Degond, Imperial College London, UK
Research interests: kinetic theory, collective dynamics, modelling, numerical simulations, applications to biology.

Dr Marie Doumic (Inria & LJLL, Sorbonne Université, France)
Research interests: inverse problems, data-driven modelling, partial-dierential equations, applications to biology.

Dr Sara Merino-Aceituno (University of Vienna, Austria)
Research interests: kinetic theory, emergent problems in biology and social sciences, interacting particle systems, modelling.

Prof Christian Schmeiser (University of Vienna, Austria)
Research interests: non-linear partial dierential equations, kinetic theory, numerics, mathematics of cell biology.
Dr Anna Kicheva (IST Austria)
Integration of opposing morphogen gradients, morphogen control of tissue growth, morphogen gradient formation