Section: New Results

Tissue growth, regeneration and cell movements

Single-cell-based models of tumor growth and tissue regeneration and embryonic development

Participants : Alexander R.A. Anderson [ Moffitt Cancer Center, Tampa, USA ] , Augustinus Bader [ Biotechnology Dept., Univ. Leipzig ] , Anne-Céline Boulanger [ Ecole Centrale de Paris ] , Helen Byrne [ Univ. of Nottingham, UK ] , Chadha Chettaoui, Mark Chaplain [ Univ. of Dundee, UK ] , Dirk Drasdo, Rolf Gebhardt [ Univ. of Leipzig, Germany ] , Jan G. Hengstler [ Leibniz Research Center, Dortmund, Germany ] , Stefan Höhme, Isabelle Hue [ INRA ] , Nick Jagiella, Ursula Klingmüller [ German Cancer Center, Heidelberg ] , Axel Krinner, Benoît Perthame, Ignacio Ramis-Conde, Alain Roche [ Institut Gustave Roussy ] , Eckehard Schöll [ Technical Univ. of Berlin, Germany ] , Luc Soler [ IRCAD, Coordinator EU-project PASSPORT ] , Alain Trubuil [ INRA ] , Irène Vignon-Clémentel [ REO project-team ] , Juhui Wang [ INRA ] , William Weens.

Structure formation in tissues as well as mal-functions on the multi-cellular level are inherently of multi-scale nature. Modifications on the molecular level by intrinsic or extrinsic factors affect the architecture and function on the multi-cellular tissue level. Much of the current research so far focuses on the analysis of intracellular pathways, genetic and metabolic regulation on the intracellular scale and on continuum equations for local densities of cells to capture multi-cellular objects on large spatial scales but only recently increasing effort is made on the interface between both: individual cell based models (IBMs) which permit to include the molecular information on one hand and to extrapolate to the multi-cellular tissue level on the other hand and hybrid models that combine continuum with individual-based models for different components.

Figure 1. Growth scenario of a tumor in a vascular network (red) that is remodelled by angiogenesis (c). Yellow: proliferating cells, green: quiescent cells, blue: necrotic region. (From [36] )

Figure 2. Image processing of confocal and bright field microscopy (first line) was used to quantify the regeneration process of liver after intoxication with the drug CCl₄ and to set up a mathematical model. Simulations with this model were directly be compared with the experimental results (second line) (red: micro-vessels, brown: hepatocytes (dark: proliferating, light: quiescent), white: necrotic lesion).

In order to fill the existing gap we have studied intracellular regulation networks [52] , [47] , multi-scale IBMs where intracellular regulation and differentiation was explicitly represented within each individual cell [54] , [24] , [29] , lattice-free IBMs [45] and continuum models that can capture their large scale behavior [7] , and cellular automaton (CA) models where each lattice site can be occupied either by at most one cell [40] or by many cells [28] , [36] and their corresponding continuum equation [44] .

Besides the methodical aspects we focus on a number of applications:

• unstructured cell populations growing in monolayer [45] , [48] .

• multicellular spheroids [45] , [46]

• vascular tumor growth (Fig. 1 )

• regulatory and evolutionary aspects in tumor growth [23] ,

• cell differentiation and lineage commitment of mesenchymal stem cells [24] , [35]

• complex tissue architectures in regenerative tissues such as the regeneration of liver lobules after toxic damage [51] , [50] (also: Höhme et. al., PNAS, in revision). (Fig. 2 ; within the German BMBF-funded network ”Systems Biology of the Hepatocyte”), liver regeneration after partial hepatectomy and cancer development in liver.

• early morphogenesis (trophoblast development)

The applications are guided by quantitative comparisons to experimental data either from published knowledge or generated by experimental partners. One main focus is on the understanding of mechanisms that control the growth dynamics and growth phenotypes of multi-cellular systems and use these later to predict and optimize therapy or biotechnological growth processes.

The adjustment of the models developed to applications requires data analysis both, of molecular data such as gene expression profiles and of image data such as spatial-temporal growth pattern. For this purpose we recently considered the geometric and topological measures to quantify tumor shapes [55] , and developed an image processing chain to quanitatively analyze liver regeneration processes in liver lobules [50] (also: Höhme et. al., PNAS, in revision).

Current and future directions include a stronger focus on models of in-vivo systems(within the German medical systems biology consortium ”LungSys” (lung cancer treatment); in collaboration which Institut Gustave Roussy, and within the EU-network ”CancerSys” (cancerogenesis in liver)). Modeling cancer development requires to take into account invasion, mutations and angiogenesis, three hallmarks of cancer and of linking the molecular to the multicellular scale [36] . Moreover, we extend the topic of liver regeneration to regeneration after partial hepatectomy (within the EU-project ”Passport”), and extend our modeling activities to understand early embryonic development (Trophoblast development, collaboration with INRA).

Cell communities self-organisation

Participants : Vincent Calvez [ ENS Lyon ] , Thomas Lepoutre, Americo Marrocco, Benoît Perthame, Christian Schmeiser, Nicolas Vauchelet.

Our activity on cell communities self-organisation has been motivated by collaborations with a team of biologists (I. B. Holland, S. Séror, Institut de Génétique et Microbiologie, CNRS UMR 8621, Univ. Paris-Sud, F-91405 Orsay) and with a team of biophysicists (A. Buguin, J. Saragosti, P. Silberzan, Institut Curie, UMR CNRS 168 "Physico-Chime-Curie).

We have continued to investigate macroscopic models at the scale of the full cell population taking into account cell motion and communications through chemo-attractant and repellent. Models which have been investigated are of the type

(1)

Here c_a and c_r represent the concentration of chemoattractant and chemorepellent respectively. These are assumed to diffuse according to Einstein's rule with coefficients d_a and d_r , they are degraded with the rates _a and _r (depending possibly on the cell population densities u and w ), and they are secreted by the cells with rates _a and _r . Their actions are represented by Fokker-Planck terms in the equation for u , as in the classical Keller-Segel model. A critical comparison between the numerical solution to system (1 ) and experimental bacterial colonies of B. subtilis are described in [27] .

Figure 3. Typical result obtained for a numerical simulation with a system of type (1 ). Isovalues snapshots of various quantities during the evolution process. Total cell density (u + w ), Active cells (u ), Chemoattractant (c_a ) and chemorepellent (c_r ).

In order to improve these types of models it is necessary to consider the detailed behaviour of individual cells in response to external stimuli. This is the purpose of kinetic models of cell populations and in particular the variants proposed recently by Y. Dolak and C. Schmeiser [43] . The theory and the numerics of such models has been investigated by N. Vauchelet who shows that the blow-up patterns at the kinetic level are different from those of the Keller-Segel system. Blow-up bands are possible and not only pointwise blow-up.

The individual based kinetic models also lead to macroscopic extensions of the Keller-Segel system that we are currently using to reproduce several experimental observations for E. coli at Institut Curie, UMR CNRS 168, and in particular traveling pulses with asymmetric profiles.