Section: Research Program
Research axis 5: Growth, evolution and regeneration in populations and tissues
Luis Almeida, Pierre-Alexandre Bliman, Marie Doumic, Dirk Drasdo, Benoît Perthame, Nicolas Vauchelet
The applications in this category span very different subjects from amyloid diseases, dengue fever, wound healing, liver regeneration and toxicity, up to bacterial growth. As the applications, the methods span a wide range. Those concerning identification of models and parameters with regard to data have partially been outlined in axis 3. Focus in this axis is on the model contribution to the biologically and/or medically relevant insights and aspects.
Liver-related modelling is partially performed within the Inria team MIMESIS (Strasbourg) with the focus on real-time, patient-specific biomechanical liver models to guide surgery and surgeons. Internationally, spatial temporal liver related models are developed in Fraunhofer MEVIS (Bremen), by T. Ricken (TU Dortmund), and P. Segers group (Leuven). Different from these, Mamba has a strong focus on spatial-temporal modelling on the histological scale, integration of molecular processes in each individual cell, and single-cell (agent) based models. Works by Schliess ,  have been highlighted in editorials.
Mathematical modelling of protein aggregation is a relatively recent domain, only a few other groups have emerged yet; among them we can cite the Inria team Dracula, with whom we are in close contact, and e.g., the work by Jean-Michel Coron (UPMC) and Monique Chyba (Hawaii, USA) in control, and Suzanne Sindi (USA) for the modelling of the yeast prion. We have interactions with all these groups and organised a workshop in June 2017, gathering both the biophysics and applied mathematics communities.
Application to protein aggregation in amyloid diseases is a long-standing interest of Mamba, dating back to 2010 , and developed through the collaboration with Human Rezaei's team at Inra. More recently, with Wei-Feng Xue in Canterbury, we investigated the intrinsic variability among identical experiments of nucleation , , Sarah Eugène's Ph.D subject (co-supervised by Philippe Robert) .
In collaboration with Tom Banks first ,  and then Philippe Moireau, we developed quantitative comparisons between model and data. Through data assimilation and statistical methods , we proposed new models and mechanisms.
The spread of certain strains of the intracellular parasitic bacterium Wolbachia in populations of mosquitoes Aedes aegypti drastically reduces their competence as vector of dengue and other severe mosquito-borne viral diseases. In the absence of a vaccine, or of any preventive or curative treatment, the release of mosquitoes deliberately infected in laboratory by this bacterium has been recently considered a promising tool to control these diseases. Technically the situation can be described by a bistable model, and the issue consists in moving from a Wolbachia-free equilibrium to a fully contaminated equilibrium.
When implementing such a method, an important issue concerns the spatial propagation of the mosquitoes: on releasing infected mosquitoes in a given domain (which can be part of a city), the hope is to invade the whole area. The study of this propagation phenomena falls into the study of existence of travelling waves.
We studied cell motion in epithelial gap closure, a form of collective cell migration that is a very widespread phenomenon both during development and adult life - it is essential for both the formation and for the maintenance of epithelial layers. Due to their importance, in vivo wound healing and morphogenetic movements involving closure of holes in epithelia have been the object of many studies. In our works (ravasio:hal-01245750, vedula:hal-01298859) we considered wound healing and epithelial gap closure in both in vivo (in particular drosophila pupa) and in vitro (MDCK cell and human keratinocytes). We found some similarities in the geometry dependence of the wound closure strategies between these two situations, indicating the existence of conserved mechanisms that should be widespread across living beings.
An integrated model, coupling a spatial-temporal model of liver regeneration after drug-induced damage to a compartment model of detoxification blood from ammonia, identified the lack of an ammonia detoxifying reaction in the biochemical consensus scheme . Hyperammonia is the most frequent reason for death due to acute liver failure in UK and USA. The spatial model represents liver micro-architecture in a group of liver lobules, the repetitive anatomical and functional units of liver, mimicking each hepatocyte as single agent and blood vessels as a network of chains of spherical objects. This model had previously predicted the subsequently validated orientation of dividing hepatocytes along the liver capillaries as order mechanism. It was here coupled to ODEs for metabolites participating in the zonated ammonia metabolism by calculating the volume of each liver lobule zone with time during regeneration after drug induced damage, which is an input parameter for the detoxification compartment model. Experiments triggered by the model predictions could identify later a candidate ammonia sink mechanism which in a follow-up work  could be shown to be the most likely mechanism compared with alternative explanations (see axis 3). This mechanism could be validated, and led to a possible therapy option in treatment of hyperammonemia.
The models have been further expanded towards true multilevel-multiscale models that include molecular HGF control of cell cycle progression (unpublished) and ammonia detoxification (Géraldine Cellière's PhD thesis, 2016; Noémie Boissier's PhD thesis, 2018). In these models, the intracellular models were executed in each individual hepatocyte, and transport of molecules with blood were simulated. Blood flow was modelled by Poiseuille law in the entire capillary network. Further conditions could be identified, under which standard pharmacokinetics-pharmacodynamics (PKPD) models fail to predict the correct dynamics and need to be replaced by spatial temporal models representing organ microarchitecture. The model has further been extended towards bile flow.
Toxicity extrapolation from in vitro to in vivo
In vivo toxicity prediction from in vitro data is a major objective in toxicology as it permits bypassing animal experiments. The multilevel-multi scale approach outlined above has been used to explore a strategy to predict the in vivo damage of paracetamol (acetaminophen) from in vitro experimental data. Model simulations and data obtained so far strongly suggest that the prediction is quantitative, if the time development of the toxicity in vitro is displayed (this is so far not common), differences in the concentration kinetics of drug metabolising enzymes in vitro are measured, and micro-architecture is determined (Géraldine Cellière's PhD thesis ). Common strategies in toxicology based on relating the maximum drug concentration or area under the drug concentration - time curve between in vitro and in vivo damage could be shown to fail.
Bacterial population growth
We exploited all the methods developed to estimate the division rate of a population (see axis 3) to address a seminal question of biology: is it a size-sensing or a timing mechanism which triggers bacterial growth? In , we showed that a sizer model is robust and fits the data well. Several studies from other groups came at the same time, showing a renewed interest on a question dated back to Jacques Monod's PhD thesis (1941). Of special interest is the “adder” model, for which we are currently developing new estimation methods.
Dengue control by releasing Wolbachia infected mosquitoes Maria Soleda Aronna, F.C. Coelho (Fundação Getulio Vargas, Brazil); D. Villela, C. Struchiner (Fiocruz, Brazil); Jorge Zubelli (IMPA, Brazil); Alain Rapaport (INRA-Montpellier), Y. Dumont (CIRAD-Montpellier); Ch. Schaerer (UNA, Paraguay).
Protein aggregation in amyloid diseases: Human Rezaei's team at Inra Jouy-en-Josas (France) and W-F Xue's team in at university of Kent (Great Britain); Tom Banks at the North Carolina State University (USA), Philippe Moireau (M3DISIM) and Philippe Robert (Rap) in Inria
Wound healing: Patrizia Bagnerini (Genova, Numerical methods), Benoît Ladoux (Institut Jacques Monod et Mechanobiology Institute Singapore, Biophysics) and Antonio Jacinto (CEDOC, Lisbon, Biology and Medicine).