Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering

Gerasimos G.  Rigatos; Efthymia G.  Rigatou; Jean Daniel  Djida

doi:10.3934/mbe.2015.12.1017

Article Contents

2015, Volume 12, Issue 5: 1017-1035. Doi: 10.3934/mbe.2015.12.1017

This issue Previous Article Order reduction for an RNA virus evolution model Next Article Analysis of a cancer dormancy model and control of immuno-therapy

Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering

1.
Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras
2.
Dept. of Paediatric Haematology-Oncology, Athens Children Hospital Aghia Sofia, 11527, Athens
3.
Department of Physics, University of Ngaoundere, P.O. Box 454 Ngaoundere

Received: January 31, 2015

Revised: January 31, 2015

Published: May 2015

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Abstract

A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of $\chi^2$ change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies)

Keywords:

Mathematics Subject Classification: Primary: 37N25 Dynamical systems in biology, 93E10 Estimation and detection, 93E11 Filtering; Secondary: 57R50 Diffeomorphisms.

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