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Planning identification experiments for cell signaling pathways: An NF[...]B case study

Fujarewicz K.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

773-780

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 NF[...]B 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.

Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes

Śmieja J.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 4

781-788

The paper deals with the analysis of signaling pathways aimed at uncovering new regulatory processes regulating cell responses. First, general issues of comparing simulation and experimental data are discussed, and various aspects of data normalization are covered. Then, a model of a particular signaling pathway, induced by Interferon-\beta, is briefly introduced. It serves as an example illustrating how mathematical modeling can be used for inferring the structure of a regulatory system governing the dynamics of intracellular processes. In this pathway, experimental results suggest that a hitherto unknown process is responsible for a decrease in the levels of one of the important molecules used in the pathway. Then, equilibrium points of the model are analyzed, allowing the rejection of all but one explanation of the phenomena observed experimentally. Numerical simulations confirm that the model can mimic the dynamics of the processes in the pathway under consideration. Finally, some remarks about the applicability of the method based on an analysis of equilibrium points are made.

Model based analysis of signaling pathways

Śmieja J.

International Journal of Applied Mathematics and Computer Science

2008

Vol. 18, no 2

139-145

The paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including unknown processes activating gene transcription by means of first-order lag elements is introduced and discussed. Then, a particular interferon-ß induced pathway is introduced, limited to early events that precede activation of gene transcription. It is shown how to simplify the system description based on the goals of modeling. Further, a computational analysis is presented, facilitating better understanding of the mechanisms underlying regulation of key components in the pathway. The analysis is illustrated by a comparison of simulation and experimental data.