Section: Application Domains

Protein polymerisation

Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with various human neurodegenerative diseases such as Alzheimer's, Parkinson's, Prion (in particular variant Creutzfeldt-Jakob disease, epidemically linked to bovine spongiform encephalopathy, or so-called “mad cow”, disease), Huntington's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials.

However, the mechanisms of polymerisation are far from being quantitatively understood by biologists. They can be modelled with the help of coagulation-fragmentation equations, a field of expertise of MAMBA [16], [36], or with stochastic models [20]. One difficulty of this application is that the reactions imply both very small and very large scales for the sizes of polymers [7], experimental data giving only access to the time evolution of size-averaged quantities [6]. Moreover, there exists an intrinsic variability among experiments, which has to be distinguished from a lack of reproducibility [20].

The European starting grant SKIPPER${}^{AD}$ involves a long-term collaboration with Human Rezaei's team, a biologist expert group in amyloid diseases at INRA Jouy-en-Josas. It allowed us to further develop new collaborations, in particular with Wei-Feng Xue's team in Canterbury, who is one of the rare biophysicists in this area who is able to measure not only size-averaged quantities, as for instance the time-evolution of the total polymerised mass, but also size distribution of polymers (at least over a certain threshold). Such measurements allow us to use much more powerful inverse problems and data assimilation methods [6].

Moreover, this field of applications to human neurogenerative diseases brings us new questions [17], which is a stimulation for our mathematical research and at the same time allows us to provide biologists with a new and efficient tool.