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Planning identification experiments for cell signaling pathways: An NFκB case study

100%
Fujarewicz K.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 4
773-780
EN
Mathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear ordinary differential equations (ODEs). It is very difficult to obtain a proper model. There are many hypotheses about the structure of the model (sets of variables and phenomena) that should be verified. The next step, fitting the parameters of the model, is also very complicated because of the nature of measurements. The blotting technique usually gives only semi-quantitative observations, which are very noisy and collected only at a limited number of time moments. The accuracy of parameter estimation may be significantly improved by a proper experiment design. Recently, we have proposed a gradient-based algorithm for the optimization of a sampling schedule. In this paper we use the algorithm in order to optimize a sampling schedule for the identification of the mathematical model of the NFκB regulatory module, known from the literature. We propose a two-stage optimization approach: a gradient-based procedure to find all stationary points and then pair-wise replacement for finding optimal numbers of replicates of measurements. Convergence properties of the presented algorithm are examined.
2
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Selecting differentially expressed genes for colon tumor classification

63%
Fujarewicz K., Wiench M.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 3
327-335
EN
DNA microarrays provide a new technique of measuring gene expression, which has attracted a lot of research interest in recent years. It was suggested that gene expression data from microarrays (biochips) can be employed in many biomedical areas, e.g., in cancer classification. Although several, new and existing, methods of classification were tested, a selection of proper (optimal) set of genes, the expressions of which can serve during classification, is still an open problem. Recently we have proposed a new recursive feature replacement (RFR) algorithm for choosing a suboptimal set of genes. The algorithm uses the support vector machines (SVM) technique. In this paper we use the RFR method for finding suboptimal gene subsets for tumornormal colon tissue classification. The obtained results are compared with the results of applying other methods recently proposed in the literature. The comparison shows that the RFR method is able to find the smallest gene subset (only six genes) that gives no misclassifications in leave-one-out cross-validation for a tumornormal colon data set. In this sense the RFR algorithm outperforms all other investigated methods.
3
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Optimal Control in a Model of Chemotherapy-induced Radiosensilisation

51%
Bajger P., Fujarewicz K., Świerniak A.
Mathematica Applicanda
|
2019
|
tom 47
|
nr 1
EN
  In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.
4
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Prediction of lung cancer patients’ response to combined chemo-radiotherapy using a personalized hybrid model

39%
Wołkowicz S., Fujarewicz K., Kurpas M., Łakomiec K., Śmieja J., Suwiński R., Świerniak A.
Mathematica Applicanda
|
2019
|
tom 47
|
nr 2
PL
The paper presents a novel approach to prediction of the combined therapy outcome for non-small lung cancer patients. A hybrid model is proposed, consisting of two parts. The first one is a mathematical model of tumor response to therapy, whose parameters are estimated by a neural network based regressor, constituting the second component of the hybrid model. Estimation is based on data from mass spectrometry of patient blood plasma samples. Comparison of clinical and simulation-based survival curves is used to evaluate the quality of the model.
EN
The paper presents a novel approach to the prediction of the combined therapy outcome for non-small lung cancer patients. A hybrid model is proposed, consisting of two parts. The first one is a mathematical model of tumor response to therapy, whose parameters are expressed as linear function of data from massspectrometry of patient blood plasma samples. These linear functions constitute thesecond component of the hybrid model. A comparison of clinical and simulation-based survival curves is used to evaluate the quality of the model.
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