Section: New Results

Tissue growth, regeneration and cell movements

Chemotaxis, self-organisation of cell communities (KPP-Fisher and Keller-Segel)

Participants : Nikolaos Bournaveas [Univ. Edinburgh] , Axel Buguin [UPMC, Institut Curie] , Vincent Calvez [ENS Lyon] , François James [univ. Orléans] , Alexander Lorz, Grégoire Nadin [UPMC] , Benoît Perthame, Jonathan Saragosti [Institut Curie] , Pascal Silberzan [Institut Curie] , Min Tang [Shanghai Jiaotong University] , Nicolas Vauchelet.

Chemotaxis denotes the ability of some cells to undergo a directed movement in response to an extracellular chemical substance. A mathematical description of chemotaxis is a major issue in order to understand collective movements of bacterial colonies. Numerous mathematical models, at various scales, have been proposed, allowing for a good description of cell aggregation under chemotaxis at the macroscopic level, the first of all being that of Keller-Segel (1971), that is now at the centre of an abundant international scientific literature.

At the cell scale, one uses kinetic equations. Numerical simulations have been performed and blow-up is also observed, which differs highly from pointwise blow-up in parabolic models. Representing them leads to various theoretical questions and amounts to define measure solutions [25] , [24] or to develop an existence theory.

Single-cell-based and continuum models of avascular tumours

Participants : Ibrahim Cheddadi, Dirk Drasdo, Benoît Perthame, Min Tang [Shanghai Jiaotong University] , Nicolas Vauchelet, Irène Vignon-Clémentel [REO project-team] .

The recent biomechanical theory of cancer growth considers solid tumours as liquid-like materials comprising elastic components. In this fluid mechanical view, the expansion ability of a solid tumour into a host tissue is mainly driven by either diffusion of cells (emerging on the mesoscopic scale by coarse graining from the cell micro-motility) or by cell division depending either on the local cell density (contact inhibition), on mechanical stress in the tumour, or both. For the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modelling, we prove there are always travelling waves above a minimal speed and we analyse their shapes. They appear to be complex with composite shapes and discontinuities. Several small parameters allow for analytical solutions; in particular the incompressible cells limit is very singular and related to the Hele-Shaw equation. These singular travelling waves are recovered numerically. See [32] .

Single cell-based models of tumour growth, tissue regeneration

Participants : Gregory Batt [CONTRAINTES project-team] , François Bertaux, Géraldine Cellière, Chadha Chettaoui, Ibrahim Cheddadi, Dirk Drasdo, Adrian Friebel, Rolf Gebhardt [Univ. of Leipzig, Germany] , Adriano Henney [Director Virtual Liver Network and VLN consortium] , Jan G. Hengstler [Leibniz Research Centre, Dortmund, Germany and CANCERSYS consortium] , Stefan Höhme, Elmar Heinzle [University of Saarbrücken and NOTOX consortium] , Isabelle Hue [INRA] , Nick Jagiella, Ursula Klingmüller [German Cancer Centre, Heidelberg and LungSys Consortium] , Axel Krinner, Johannes Neitsch, Benoît Perthame, Ignacio Ramis-Conde, Luc Soler [ IRCAD, Coordinator EU-project PASSPORT and PASSPORT consortium] , Jens Timmer [University of Leipzig, Germany] , Irène Vignon-Clémentel [REO project-team] , Juhui Wang [INRA] , William Weens.

A Multi-scale model for clonal competition in growing tumours

In this work we set up a multi-scale model testing the impact of three experimentally found variants of a signal transduction pathway controlling cell-cell adhesion on multi-cellular growth as well as the possible consequences of inhomogeneous populations where each of the three phenotypes competed [30] .

Growth of cell populations in embedding granular and cell-like matter

In this work simulations of growing 2D and 3D clones embedded in granular and cell-like matter were mimicked [21] . The influence of active directed cell motion vs. passive pushing triggered by cell proliferation, as well as of various parameters of the embedding matter, such as the friction of embedding objects with its environment, adhesion strength, size of objects, elastic modulus etc. on the growth kinetics and the spatial pattern has been studied. The emerging patterns are strongly reminiscent of a fingering instability (a type of a Saffman-Taylor instability) occuring if a viscous fluid is injected into a more viscous fluid constrained between two plates (Hele Shaw cell).

Quantitative modelling of multi-cellular spheroids

Nick Jagiella in his thesis has worked out how stepwise and iteratively mechanisms controlling the spatial-temporal growth dynamics can be inferred by combining information from bright field micrographs stained for proliferating, dying cells, cell nuclei and extra-cellular matrix with the macroscopic growth kinetics.

This thesis, pursued within the German network project LUNGSYS was defended in September 2012. The thesis work was mainly supervised by Dirk Drasdo, PI for this part within the LUNGSYS project. Main collaborators were Margareta Mueller (previously DKFZ, Heidelberg) and Ursula Klingmueller, (DKFZ Heidelberg).

Moreover, Géraldine Cellière has worked out a model to mimic the aggregation of cells in the hanging drop method, a standard method to generate 3D multi-cellular aggregates. The kinetics and final configuration give information on multicellular aggregates. This work is pursued within the EU NOTOX project. Main collaborators are Fozia Noor and Elmar Heinzle (Univ. of Saarbruecken).

Image reconstruction of 3D liver architecture at subcellular level

In order to permit simulation liver function we started to set up an image processing pipeline resolving liver at subcellular scale. This will enable us to mimic all flows in liver, which comprises of blood flow through the micro-vessels (sinusoids), of blood plasma through the space between micro-vessel wall and hepatocytes, the main type of liver cells (called space of Disse), and of the bile through a network of bile canaliculi. Besides image analysis, also setting up the models of the flows has been started.

This work is conducted by the PhD student Adrian Friebel (IZBI, University of Leipzig) co-supervised by Dirk Drasdo and Stefan Hoehme (IZBI, University of Leipzig) within the Germany funded grant project Virtual Liver Network (VLN; PI from IZBI, Leipzig: Dirk Drasdo). Main collaborator is Jan G. Hengstler from the IfADo (directeur at the Leibniz Institute in Dortmund, Germany).

Ammonia metabolism during liver regeneration

Based upon the paper on liver regeneration after drug-induced damage (Hoehme et. al. PNAS 2010 [55] ) we in a next step investigated the change of ammonia metabolism during the regeneration process. Ammonia is toxic for the body. We linked our spatial-temporal liver lobule model with a compartment model for the ammonia, glutamine and urea metabolism. In the latter we consider a compartment (the peri-central compartment) in which glutamine synthetase, a strongly ammonia-detoxifying enzyme, is degraded efficiently and a (peri-portal) compartment, in which this is not the case. By testing different hypotheses on the chemical reactions taking place during the degradation process and quantitatively comparing to time-space data of the regeneration process including data on the activity of glutamine synthetase we were able to propose a potentially missing chemical reaction. Validation experiments have been started and suggest that the original reaction scheme was indeed incomplete.

This work is conducted by Dirk Drasdo and Stefan Hoehme (IZBI, University of Leipzig) partly within the Germany funded grant project Virtual Liver Network (VLN; PI from IZBI, Leipzig: Dirk Drasdo) and the EU project NOTOX. Main collaborators are Rolf Gebhardt (chair for Biochemistry, University of Leipzig), Jan G. Hengstler from the IfADo (Leibniz Institute in Dortmund, Germany) and BioControl Jena GmbH, a company in Jena, Germany.

Multi-scale simulation of cell cycle progression during liver regeneration

In previous work on liver regeneration after drug induced damage (Hoehme et. al. PNAS 2010 [55] ) the experimentally observed spatial-temporal proliferation pattern has been used as an input parameter. We have now started to study the molecular control of cell cycle progression by hepatocyte growth factor (HGF). Based on model predictions with a hypothesized model linking the downstream activation of the HGF-pathway with cell cycle progression, experiments were performed which now led to a validated intracellular model of cell cycle progression by HGF. Moreover, based on model simulations predicting that two sources of HGF are necessary to explain the experimentally observed proliferation pattern, experiments detecting the potential sources of HGF have been initiated. The models are multi-scale in that the precise spatial architecture of a piece of liver tissue is modelled representing each individual hepatocyte as well as the blood micro-vessels. A system of ODE's mimicking the HGF signalling and its impact on cell cycle progression is solved inside each individual cell. The project works out a systematic strategy to stepwise identify multi-scale multi-level processes in tissue organisation extending the lines pursued in Hoehme et. al. [55] and Holzhuetter et. al. [23] .

This work is conducted by Dirk Drasdo and Stefan Hoehme (IZBI, University of Leipzig) within the Germany funded grant project Virtual Liver Network (VLN; PI from IZBI, Leipzig: Dirk Drasdo). Main collaborators are Ursula Klingmueller and Lorenza D'Alessandro (UK is Professor at Heidelberg University and department head at German Cancer Research Centre (DKFZ), Heidelberg, Germany) as well as Jens Timmer and Andreas Raue (JT is Professor University of Freiburg, Germany).

Phenotypes in early liver cancer

The model of a liver lobule, the smallest functional unit of liver (Hoehme et. al., PNAS 2010 [55] ) has been used as a starting point to explain the experimentally observed early tumour phenotypes. We made a sensitivity analysis to identify the parameters that influence the tumour phenotype. Each simulation mimicked a monoclonal tumour. We could show that the observed early phenotypes could be explained by only a few sensitive parameters which are the direction of cell division, cell-micro-vessel adhesion, and destruction of micro-vessels by the tumour cells.

This work has been taken over from the previous PhD student William Weens by the PhD student François Bertaux who is co-supervised by Dirk Drasdo and Gregory Batt. Main collaborator is Jan G. Hengstler from the IfADo (directeur at the Leibniz Institute in Dortmund, Germany).

Regeneration of liver after partial hepatectomy

We continued this earlier activity by initiating experiments on pigs to test the model prediction that the 2nd wave of proliferation during regeneration after partial hepatectomy in pig should occur only close to the Glisson capsule, that encloses the liver, while in mouse proliferation occurs homogeneously and isotropically distributed over the whole liver lobe.

This work is conducted by Dirk Drasdo and Stefan Hoehme (IZBI, University of Leipzig) within the Germany funded grant project Virtual Liver Network. Main collaborators are Jan G. Hengstler from the IfADo (Leibniz Institute in Dortmund, Germany) and Eric Vilbert, Centre Hépato-Biliaire (CHB)- INSERM U785$$, Hospital Paul Brousse, Villejuif.

High resolution model for eukaryotic cells

In order to permit simulations directly out of 3D reconstructions of confocal laser scanning micrographs at subcellular resolution we developed a model that is capable to resolve complex cell shapes. The model parameters were calibrated by comparison with experiments probing the material properties of cells. Moreover, the cell division was implemented. The model was integrated into the CellSys software.

This work is conducted by the PhD student Johannes Neitsch (IZBI, University of Leipzig) co-supervised by Dirk Drasdo and Stefan Hoehme (IZBI, University of Leipzig) within the Germany funded grant project Virtual Liver Network (VLN). Main collaborators are Jan G. Hengstler from the IfADo (directeur at the Leibniz Institute in Dortmund, Germany) and Josef Kaes (Prof. for Experimental Physics, Univ. Leipzig).

Yeast cells playing the Game of Life

Within a collaboration with a synthetic biology lab at MIT, we work on the multicellular modelling of engineered yeast cell populations. Those cells secrete a messenger molecule (IP) which diffuse in the medium, bind to other cells, and trigger a signalling cascade which finally induce expression of lethal genes. A model has been established based on our single-cell-based model framework associated with PDE's simulations, and it is currently used to explain and guide experiments obtained at MIT.

This work is conducted within the project Sine2Arti by François Bertaux co-supervised by Gregory Batt and Dirk Drasdo, and by Szymon Stoma. Main collaborator is Ron Weiss, MIT, Boston, USA.

Stochastic modelling of extrinsic apoptosis

Here we extended a well-established ODE model of TRAIL-induced apoptosis developed by Sorger's group in Harvard by the possible effect of cell-to-cell variability due to stochasticity of rare events in the cascade.

This work is conducted within the project Sine2Arti by François Bertaux co-supervised by Gregory Batt and Dirk Drasdo, and by Szymon Stoma as well as Xavier Duportet for the experimental part.

Artificial Homeostasis in HeLa cells

The aim is to genetically engineer human cancer cells (HeLa cell line) such that they perform population control in a petri dish. To do so, it is made use of extrinsic apoptosis by forcing cells to produce a messenger molecule able to trigger apoptosis above a certain threshold concentrations in the medium. We developed a mathematical model which integrates both PDEs and intracellular components into a single-cell-based model framework. Such model allows to help designing the genetic system that should be integrated into cells as well as guiding experiments.

This work is conducted within the project Sine2Arti by François Bertaux who is co-supervised by Gregory Batt and Dirk Drasdo. Moreover Szymon Stoma for the modelling part, as well as Xavier Duportet for the experimental part from the CONTRAINTES team are included.

Modelling flow in tissues

Participants : Lutz Brusch [TU Dresden] , Dirk Drasdo, Adrian Friebel [IZBI, University of Leipzig] , Stefan Hoehme [IZBI, University of Leipzig] , Nick Jagiella [Inria and IZBI, University of Leipzig] , Hans-Ulrich Kauczor [University of Heidelberg, Germany] , Fabian Kiessling [University Clinics, Technical University of Aachen, Germany] , Ursula Klingmueller [German Cancer Research Centre (DKFZ), Heidelberg, Germany] , Hendrik Laue [Fraunhofer Mevis, Bremen, Germany] , Ivo Sbazarini [MPI for Molecular Cell Biology and Genetics, Dresden, Germany] , Irène Vignon-Clémentel [REO project-team] , Marino Zerial [MPI for Molecular Cell Biology and Genetics, Dresden, Germany] .

Flow and perfusion scenarios in cancer

In this subject we simulated typical flow and perfusion scenarios in tumour and tissue including, how the spatial-temporal pattern look like on the scale of non-invasive medical image modalities currently applied, to infer parameters that are used to or may permit to evaluate the perfusion of tumors in patients. The simulations use Poiseuille flow and Kirchhoff rule in 3D blood network representing typical architectures.

The work was part of the PhD thesis of Nick Jagiella, defended in September 2012 co-supervised by Dirk Drasdo and Irene Vignon-Clementel, and conducted within the grant funded network projects LUNGSYS and LUNGSYS II. Main collaborators were Oliver Sedlaczek, DKFZ Heidelberg and University of Heidelberg, Fabian Kissling, Technical University of Aachen and Hendrik Laue, Fraunhofer Mevis, Bremen (all in Germany).

Flow in liver lobules

The aim of this project is to simulate realistically the flow of matter within liver lobules from images generated with different image modalities at histological scales. So far we have established a model of blood flow and perfusion in liver lobules based upon 3D reconstruction of confocal micrographs.

This work is conducted by collaboration of different groups within the Germany funded grant project Virtual Liver Network. From our group Nick Jagiella, Adrian Friebel, and Stefan Hoehme, Dirk Drasdo are involved, main collaborators are Irene Vignon-Clementel (REO project team Inria), Marino Zerial and Ivo Sbazarini (Max-Planck Institute for Molecular Cell Biology and Genetics, Dresden, Germany), Lutz Brusch (Technical University of Dresden) and Jan G. Hengstler from the IfADo (Leibniz Institute in Dortmund, Germany).

Contraction of acto-myosin structures in morphogenesis and tissue repair

Participants : Luís Almeida, P. Bagnerini [Univ. Genova] , A. Habbal [Univ. Nice] , A. Jacinto [CEDOC, Lisbon] , M. Novaga [Univ. Padova] , A. Chambolle [École Polytechnique] , J. Demongeot [Univ. Grenoble] .

Contraction of actin structures (in one, two or three dimensions) plays an important role in many cellular and tissue movements, both at a multicellular tissue level and at a cellular (and even intracellular) one: from muscle contraction to neural tube closure, epiboly in zebrafish embryo, the contractile ring in cytokinesis, cell crawling,... examples are everywhere in the living world. These structures consist of meshworks of actin filaments (which are like fibers) that are cross-linked by molecular motors (Myosin II) which can make the actin filaments slide relative to each other, thus generating deformation movements.

In [4] we are particularly interested in modelling the contraction of acto-myosin cables in morphogenesis and tissue repair. The experiments done in collaboration with A. Jacinto's lab show that the local curvature (and in particular its sign) plays an important role in the contractile behaviour of the acto-myosin cables. These experimental results led us to develop some of these ideas in [6] and to do a more abstract study of flows by the positive part of the curvature in [5] .