Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering
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 int...
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AIMS Press
2015-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1017 |
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| author | Gerasimos G. Rigatos Efthymia G. Rigatou Jean Daniel Djida |
| author_facet | Gerasimos G. Rigatos Efthymia G. Rigatou Jean Daniel Djida |
| author_sort | Gerasimos G. Rigatos |
| collection | DOAJ |
| description | 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) |
| format | Article |
| id | doaj-art-c3f8a23fae35431aab6d3c0b4d09b1a1 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c3f8a23fae35431aab6d3c0b4d09b1a12025-01-24T02:33:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-05-011251017103510.3934/mbe.2015.12.1017Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filteringGerasimos G. Rigatos0Efthymia G. Rigatou1Jean Daniel Djida2Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion PatrasDept. of Paediatric Haematology-Oncology, Athens Children Hospital Aghia Sofia, 11527, AthensDepartment of Physics, University of Ngaoundere, P.O. Box 454 NgaoundereA 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)https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1017statistical change detectionintracellular protein synthesis dynamical systemdifferential flatness theoryp53 protein - mdm2 inhibitor modelearly diagnosis.nonlinear kalman filtering |
| spellingShingle | Gerasimos G. Rigatos Efthymia G. Rigatou Jean Daniel Djida Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering Mathematical Biosciences and Engineering statistical change detection intracellular protein synthesis dynamical system differential flatness theory p53 protein - mdm2 inhibitor model early diagnosis. nonlinear kalman filtering |
| title | Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering |
| title_full | Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering |
| title_fullStr | Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering |
| title_full_unstemmed | Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering |
| title_short | Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering |
| title_sort | change detection in the dynamics of an intracellular protein synthesis model using nonlinear kalman filtering |
| topic | statistical change detection intracellular protein synthesis dynamical system differential flatness theory p53 protein - mdm2 inhibitor model early diagnosis. nonlinear kalman filtering |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1017 |
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