Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process

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• 作者：Monique Chyba (1)
  Jean-Michel Coron (2)
  Pierre Gabriel (3)
  Alain Jacquemard (4)
  Geoff Patterson (1)
  Gautier Picot (1)
  Peipei Shang (5)
  
  1. Mathematics Department ; University of Hawai鈥榠 ; Honolulu ; HI ; 96822 ; USA
  2. Laboratoire Jacques-Louis Lions ; UMR 7598 ; Universit茅 Pierre et Marie Curie-Paris 6 ; 75005 ; Paris ; France
  3. Laboratoire de Math茅matiques de Versailles ; CNRS UMR 8100 ; Universit茅 de Versailles Saint-Quentin ; 45 Avenue des Etats-Unis ; 78035 ; Versailles ; France
  4. Institut de Math茅matiques de Bourgogne ; UMR 5584 ; Universit茅 de Bourgogne ; 9 avenue Alain Savary ; 21078 ; Dijon ; France
  5. Department of Mathematics ; Tongji University ; Shanghai ; 200092 ; China
  
• 关键词：Transmissible spongiform encephalopathies ; Nucleated polymerization ; Optimal control ; Singular extremals ; 93C95 ; 70Q05 ; 70E60
• 刊名：Acta Applicandae Mathematicae
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：135
• 期：1
• 页码：145-173
• 全文大小：1,520 KB
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• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036

文摘

Protein Misfolding Cyclic Amplification is a procedure used to accelerate the prion-replication process involved during the incubation period of transmissible spongiform encephalopathies. This technique could be used to design an efficient diagnosis test detecting the abnormally-shaped protein responsible of the decease before the affected person is at an advanced stage of the illness. In this paper, we investigate the open problem to determine what is the optimal strategy to produce maximum replication in a fixed time. Primarily, we expand on prior attempt to answer this question in general, and provide results under some specific assumptions.