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Acta Applicandae Mathematicae

, Volume 135, Issue 1, pp 145–173 | Cite as

Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process

  • Monique ChybaEmail author
  • Jean-Michel Coron
  • Pierre Gabriel
  • Alain Jacquemard
  • Geoff Patterson
  • Gautier Picot
  • Peipei Shang
Article

Abstract

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.

Keywords

Transmissible spongiform encephalopathies Nucleated polymerization Optimal control Singular extremals 

Mathematics Subject Classification

93C95 70Q05 70E60 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Monique Chyba
    • 1
    Email author
  • Jean-Michel Coron
    • 2
  • Pierre Gabriel
    • 3
  • Alain Jacquemard
    • 4
  • Geoff Patterson
    • 1
  • Gautier Picot
    • 1
  • Peipei Shang
    • 5
  1. 1.Mathematics DepartmentUniversity of Hawai‘iHonoluluUSA
  2. 2.Laboratoire Jacques-Louis LionsUMR 7598, Université Pierre et Marie Curie-Paris 6ParisFrance
  3. 3.Laboratoire de Mathématiques de VersaillesCNRS UMR 8100, Université de Versailles Saint-QuentinVersaillesFrance
  4. 4.Institut de Mathématiques de BourgogneUMR 5584, Université de BourgogneDijonFrance
  5. 5.Department of MathematicsTongji UniversityShanghaiChina

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