Optimization of an Amplification Protocol for Misfolded Proteins by using Relaxed Control

TL;DR

This paper develops an optimal control framework for enhancing an amplification method for misfolded proteins, which could improve prion disease detection, by relaxing a nonlinear control problem and solving it explicitly in certain cases.

Contribution

It introduces a relaxed control approach to an amplification protocol for misfolded proteins and provides explicit solutions for the relaxed problem in two dimensions.

Findings

Oscillations explained by Perron and Floquet eigenvalue theory.

Relaxed control problem is solvable explicitly for large final times.

Method potentially improves detection of prion diseases.

Abstract

We investigate an optimal control problem which arises in the optimization of an amplification technique for misfolded proteins. The improvement of this technique may play a role in the detection of prion diseases. The model consists in a linear system of differential equations with a nonlinear control. The appearance of oscillations in the numerical simulations is understood by using the Perron and Floquet eigenvalue theory for nonnegative irreductible matrices. Then to overcome the unsolvability of the optimal control, we relax the problem. In the two dimensional case we solve explicitely the optimal relaxed control problem when the final time is large enough.