Optimization of prion assemblies fragmentation

This work is motivated by our desire to substantially improve our understanding of prion assembly formation and spreading, which could provide a better insight into underpinnings of many neurodegenerative diseases, including Alzheimer's, Parkinson's and Prion diseases. Moreover, our investigation may help lay the foundation for designing experiments to identify key steps in the kinetic pathway of prion assembly formation which could serve as potential therapeutic targets in rational drug design. Our approach is based on employing geometric optimal control to analyze fragmentation of prion assemblies with a focus on the role of singular extremals. It may help to significantly accelerate the current amplification protocols, such as the Protein Misfolding Cyclic Amplification, and hence substantially reduce the time needed to diagnose many neurodegenerative diseases.

[1]  J. Castilla,et al.  Ultra-efficient Replication of Infectious Prions by Automated Protein Misfolding Cyclic Amplification* , 2006, Journal of Biological Chemistry.

[2]  Laurent Pujo-Menjouet,et al.  A mathematical analysis of the dynamics of prion proliferation. , 2006, Journal of theoretical biology.

[3]  H. Maurer,et al.  Sensitivity analysis of optimal control problems with bang-bang controls , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[4]  Frédéric Bonnans,et al.  Bocop - A collection of examples , 2012 .

[5]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[6]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[7]  B. Permanne,et al.  Sensitive detection of pathological prion protein by cyclic amplification of protein misfolding , 2001, Nature.

[8]  R. Tycko.  Solid-state NMR studies of amyloid fibril structure. , 2011, Annual review of physical chemistry.

[9]  M A Nowak,et al.  Quantifying the kinetic parameters of prion replication. , 1999, Biophysical chemistry.

[10]  Jean-Michel Coron,et al.  Optimization of an amplification protocol for misfolded proteins by using relaxed control , 2013, Journal of Mathematical Biology.

[11]  Martin A. Nowak,et al.  Prion infection dynamics , 1998 .

[12]  Olivier Cots.  Contrôle optimal géométrique : méthodes homotopiques et applications , 2012 .

[13]  M. Chyba,et al.  Singular Trajectories and Their Role in Control Theory , 2003, IEEE Transactions on Automatic Control.

[14]  J. Castilla,et al.  PMCA. A Decade of In Vitro Prion Replication , 2010 .

[15]  Jean-Michel Coron,et al.  Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process , 2015 .

[16]  G. Telling,et al.  Enhancement of protein misfolding cyclic amplification by using concentrated cellular prion protein source. , 2009, Biochemical and biophysical research communications.

[17]  David Eisenberg,et al.  Atomic View of a Toxic Amyloid Small Oligomer , 2012, Science.

[18]  Irina S. Alexeeva,et al.  Highly Efficient Protein Misfolding Cyclic Amplification , 2011, PLoS pathogens.

[19]  Jean-Michel Coron,et al.  Identification of the Fragmentation Role in the Amyloid Assembling Processes and Application to their Optimization , 2015, SIAM Conf. on Control and its Applications.