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access icon free Non-linear feedback control of the p53 protein–mdm2 inhibitor system using the derivative-free non-linear Kalman filter

© The Institution of Engineering and Technology
Received 09/07/2015, Accepted 17/11/2015, Revised 09/11/2015, Published 01/06/2016

It is proven that the model of the p53–mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53–mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53–mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53–mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Inspec keywords: biochemistry; perturbation theory; proteins; Kalman filters; inverse problems; molecular biophysics

Other keywords: nonmeasurable elements; perturbation compensation method; p53 protein-mdm2 inhibitor system; diffeomorphism; inverse transformation; chemotherapy schemes; feedback control law; differential flatness theory; nonlinear feedback control; protein synthesis loop; nonlinear model; modelling uncertainties; medication infusion; protein synthesis model; derivative-free nonlinear Kalman filter

Subjects: Physical chemistry of biomolecular solutions and condensed states

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