Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly

被引:13
作者
Eugene, Sarah [1 ,2 ]
Xue, Wei-Feng [3 ]
Robert, Philippe [1 ]
Doumic, Marie [1 ,2 ]
机构
[1] INRIA Paris, 2 Rue Simone Iff,CS 42112, F-75589 Paris 12, France
[2] Univ Paris 06, Sorbonne Univ, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris, France
[3] Univ Kent, Sch Biosci, Canterbury CT2 7NJ, Kent, England
基金
英国生物技术与生命科学研究理事会; 欧洲研究理事会;
关键词
SICKLE HEMOGLOBIN POLYMERIZATION; KINETICS; AGGREGATION; MECHANISM;
D O I
10.1063/1.4947472
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic differential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model offers a new perspective and paves the way for a new and efficient approach on extracting vital information regarding the key initial events of amyloid formation. Published by AIP Publishing.
引用
收藏
页数:7
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