Theory, Simulation and Observations of polymerization processes in Prion and Alzheimer diseases – TOPPAZ

Prion pathology (Bovine Spongiform Encephalopathy, commonly known as Mad-Cow Disease, or Creutzfeldt-Jakob Disease for instance) and Alzheimer Disease are both characterized by accumulation of large protein polymers, so-called 'fibrils', in the brain. The key event in the pathogenesis is the conversion of monomeric proteins, that are non pathological and naturally present in the brain, into a pathogenic conformation. This misfolded protein then gets the ability to convert other monomers and starts aggregating. Despite the huge number of studies dedicated to the biochemical description of the pathogenesis, precise polymerization mechanisms and kinetic pathways involved in the aggregation process are still unclear. The problem we propose to treat here is a mathematical modelling, numerical analysis, and comparison between simulations and experiments for prion and Alzheimer amyloid aggregation phenomena. It is a very promising field and can provide a deeper understanding of biological phenomena, as clearly show the recent articles (Greer et al 2006, Calvez et al 2008). Major aim of these models is to demonstrate that essential features of prion diseases can be explained by purely physico-chemical mechanisms, as supposed by the protein-only hypothesis. In addition, mathematical modelling allows to study the effect of very elementary processes in a separate manner, what is difficult to do experimentally, and can thus enlighten major biological issues such as oligomerization pathways. By combining theoretical and experimental approaches, we aim to establish a yet uncharacterized link between size, structure, morphology and biological properties (amyloidogenic and neuropathogenic) of amyloid polymers in prion and Alzheimer's diseases. That should help to identify the critical polymers involved in amyloid accumulation and physiopathology, which is a crucial step in therapeutic and diagnostic perspectives. We will first focus on prion polymerization, before exploring Alzheimer disease amyloid aggregation, for which less mathematical models already exist but what is already a field of active research for the INRA group, for almost two years. The mathematical work is thought in constant interaction with the INRA team of bio-physicists and biologists, to stick to the biological questions which arise, and to compare theoretical, numerical and experimental results. It is in direct continuation of the 18 month fruitful collaboration between CEA members (Franck Mouthon and Natacha Lenuzza), associated to the INRA team, and INRIA (V. Calvez, B. Perthame, M. Doumic, P. Gabriel), attested by 2 articles in press and others in progress. Polymerization mechanisms are described mathematically by fragmentation-type equations, either discrete or continuous, which are a very active current research field in mathematics, with many open questions, such as their asymptotic behaviour when nonlinearities occur (see Michel, 2007) ; how aggregation and fragmentation can equilibrate each other (see Michel, 2005) to give rise to an asymptotic steady profile, or on the contrary how dominant fragmentation can lead to concentration in size (Escobedo et al. 2005); what are the most efficient numerical schemes to solve them (Devys et al, 2008); how the proliferation rate (fitness) depends on the main coefficients (Michel, optimal, 2006) ; etc. Inverse problems in this type of equations are also a very open field, with yet very few existing works (see Perthame, Zubelli, 2007 or Doumic, Perthame, Zubelli, 2008 and references therein). To sum-up, this project gathers research groups having confirmed experience in the field and complementary skills, in order to develop mathematical and numerical tools for supporting experimentalists in the study of amyloid aggregation. We also expect mathematical progresses in the understanding of the properties of fragmentation and cell-division type equations, and their inverse problems counterparts. The mathematical team gathers members who are already used to collaborate, as attested by their numerous common articles, and whose skills are complementary: expertise in fragmentation equations with B. Perthame, P. Michel and M. Doumic; expertise in inverse problems with J. Zubelli and his group in IMPA; expertise in numerical schemes with B. Perthame and V. Calvez; etc. The INRA team has a long standing experience in Prion field. As attested by their publications since 1999 they have explored the physico-chemical aspects of Prion conformational changes. More recently the development of new biophysical tools leading to explore fibrils fragmentation and precise size distribution in complex media will lead for the first time to explore some aspects of fibrilogenesis which were, until now, poorly explored. Furthermore, The INRA team tightly collaborates with J.P Deslys and F.Mouthon from CEA, which will participate as collaborator in this project.