Final Report Summary - SKIPPERAD (Simulation of the Kinetics and Inverse Problemfor the Protein PolymERizationin Amyloid Diseases (Prion, Alzheimer’s))
The SKIPPERAD project aims at providing new mathematical models and methods to biologists, in order to help them to understand the main chain-reaction mechanisms occuring in "amyloid diseases" - a group of diseases including Alzheimer's, Parkinson's, Prion (madcow) diseases.
This led us to both mathematical and biological results.
In mathematics, we solved the problem of estimating the division rate in a population where the size of the individuals controls the division process; this used both statistical and analytical methods, which allowed us to have now a complete picture of the problem (even if some questions remain still open, for instance concerning limit cases). (2 main papers: Doumic et al, Bernoulli, 2015 and Bourgeron et al, Inverse Problems, 2014). We are now focusing on the estimation of other reaction rates: the way the polymers fragmentate (called the "fragmentation kernel" – solved theoretically in Doumic, Escobedo and Tournus, annals of the IHP, 2018), or the depolymerising rate for instance. We have also developed a general framework able to be applied to a wide variety of equations describing complex mechanisms (Armiento et al., J. Theor. Biol., 2017 and PLoS One, 2017). Finally, we also introduced a stochastic process description to understand the intrinsic variability among experimental curves (Eugène, Xue, Doumic and Robert, J. Chem. Physics, 2016, and SIAM Applied Math, 2016).
Surprisingly, the mathematical methods we developed revealed useful not only for the study of protein aggregation in amyloid diseases, but also
- for the study of bacterial growth and senescence in yeast. Notably, we showed (in Robert et al, BMC Biology) that the bacterial division was driven by the size of the bacteria rather than their age ;
- for the study of the senescence in yeast, where a mathematical model for telomere shortening (proved to be responsible for the senescence), compared to experimental data obtained by T. Teixeira and Z. Xu, deciphers the causes of heterogeneity among cells in different lineages of cells (Bourgeron, Xu, Doumic and Teixeira, Scientific Reports, 2015).
When applying our results to protein aggregation, we first obtained some negative results, establishing that a wide-spread technique (called Thioflavine T measurement) is not sufficient alone for a full understanding of chain-reaction mechanisms, which may depend on the sizes of the polymers (Banks et al, J. Biol. Dynamics, 2015). We turned then to other types of techniques – Static Light Scattering (Armiento et al, JTB 2017), size exclusion chromatography (Armiento et al., PLoS One 2017), Atomic Force Microscopy (in progress with W.F. Xue’s team). To date, our biological conclusions were the following :
- the smallest oligomers of PrP revealed to be the most stable ones (Armiento et al., J. Theor. Biol., 2017), a conclusion which rejoins direct experimental evidences and is of key importance to guide therapeutic strategies,
- there is an exchange of information between structurally distinct PrP oligomers (Armiento et al., PLoS One, 2017), leading to new models involving several polymeric species – a conclusion which in turn gave rise to a new mathematical model (Doumic, Fellner, Mezache and Rezaei, submitted).
This led us to both mathematical and biological results.
In mathematics, we solved the problem of estimating the division rate in a population where the size of the individuals controls the division process; this used both statistical and analytical methods, which allowed us to have now a complete picture of the problem (even if some questions remain still open, for instance concerning limit cases). (2 main papers: Doumic et al, Bernoulli, 2015 and Bourgeron et al, Inverse Problems, 2014). We are now focusing on the estimation of other reaction rates: the way the polymers fragmentate (called the "fragmentation kernel" – solved theoretically in Doumic, Escobedo and Tournus, annals of the IHP, 2018), or the depolymerising rate for instance. We have also developed a general framework able to be applied to a wide variety of equations describing complex mechanisms (Armiento et al., J. Theor. Biol., 2017 and PLoS One, 2017). Finally, we also introduced a stochastic process description to understand the intrinsic variability among experimental curves (Eugène, Xue, Doumic and Robert, J. Chem. Physics, 2016, and SIAM Applied Math, 2016).
Surprisingly, the mathematical methods we developed revealed useful not only for the study of protein aggregation in amyloid diseases, but also
- for the study of bacterial growth and senescence in yeast. Notably, we showed (in Robert et al, BMC Biology) that the bacterial division was driven by the size of the bacteria rather than their age ;
- for the study of the senescence in yeast, where a mathematical model for telomere shortening (proved to be responsible for the senescence), compared to experimental data obtained by T. Teixeira and Z. Xu, deciphers the causes of heterogeneity among cells in different lineages of cells (Bourgeron, Xu, Doumic and Teixeira, Scientific Reports, 2015).
When applying our results to protein aggregation, we first obtained some negative results, establishing that a wide-spread technique (called Thioflavine T measurement) is not sufficient alone for a full understanding of chain-reaction mechanisms, which may depend on the sizes of the polymers (Banks et al, J. Biol. Dynamics, 2015). We turned then to other types of techniques – Static Light Scattering (Armiento et al, JTB 2017), size exclusion chromatography (Armiento et al., PLoS One 2017), Atomic Force Microscopy (in progress with W.F. Xue’s team). To date, our biological conclusions were the following :
- the smallest oligomers of PrP revealed to be the most stable ones (Armiento et al., J. Theor. Biol., 2017), a conclusion which rejoins direct experimental evidences and is of key importance to guide therapeutic strategies,
- there is an exchange of information between structurally distinct PrP oligomers (Armiento et al., PLoS One, 2017), leading to new models involving several polymeric species – a conclusion which in turn gave rise to a new mathematical model (Doumic, Fellner, Mezache and Rezaei, submitted).