Modeling and analysis of prion dynamics in the presence of a chaperone
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- 作者：Rajiv Kumar ; Padma Murali
- 关键词：Prions ; Chaperones ; Nucleated polymerization
- 刊名：Mathematical Biosciences
- 出版年：2008
- 出版时间：May 2008
- 年：2008
- 卷：213
- 期：1
- 页码：50-55
- 全文大小：275 K
文摘
Prions are infectious agents and are polymers called T43-2&_mathId=mml1&_user=1067359&_cdi=6078&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=a31f6af8e6090728d75ff8b3042aa197"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">PrPSc—Prion protein scrapies, of a normal protein, a monomer called alt=""Click to view the MathML source"">PrPc—Prion protein cellular. These alt=""Click to view the MathML source"">PrPScs cause TSEs—transmissible spongiform encephalopathies such as bovine spongiform encephalopathy (BSE) in cattle, scrapies in sheep, Kuru and Creutzfeld–Jacob diseases in humans. Cellular molecular chaperones, which are ubiquitous, stress-induced proteins, and newly found chemical and pharmacological chaperones have been found to be effective in preventing misfolding of different disease-causing proteins, essentially reducing the severity of several neurodegenerative disorders and many other protein-misfolding diseases. In this work, we propose a model for the replication of prions by nucleated polymerization in the presence of a chaperone. According to this model, the biological processes of coagulation, splitting and the inhibitory effects of the chaperone can be described by a coupled system consisting of ordinary differential equations and a partial differential equation. The model is converted into a system of ordinary differential equations and the equilibrium points are computed and their stability is studied. We give a numerical simulation of the model and we find that a disease free state can be achieved in the presence of a chaperone. The duration of the disease free state is found to increase with the amount of chaperone and this amount of chaperone can be computed from the model.