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1

Sensitivity Analysis Aimed at Finding Potential Molecular Drug Targets

Śmieja Jarosław, Kardyńska Małgorzata, Pudlo Marta

Mathematica Applicanda

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2019

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Vol. 47, no. 2

197--205

EN

Sensitivity analysis has become one of the standard tools in analysis of models of intracellular processes. Various methods have been proposed, developer for either local or global sensitivity of systems under investigation. In this work, we propose a method that may be used to find potential molecular drug targets, taking into account heterogeneity of population of cells with respect to their responses to a particular drug agent.

PL

Analiza wrażliwości stała się jednym ze standardowych narzędzi w analizie modeli procesów wewnątrzkomórkowych. Do tej pory zaproponowano różne metody, opracowane dla lokalnej lub globalnej wrażliwości badanych systemów. W niniejszej pracy proponujemy metodę, która może być wykorzystana do znalezienia potencjalnych molekularnych celów leków, biorąc pod uwagę heterogeniczność populacji komórek w odniesieniu do ich odpowiedzi na konkretny lek.

2

Sensitivity analysis of signaling pathway models based on discrete-time measurements

Kardynska M., Smieja J.

Archives of Control Sciences

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2017

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Vol. 27, no. 2

239--250

EN

The paper is focused on sensitivity analysis of large-scale models of biological systems that describe dynamics of the so called signaling pathways. These systems are continuous in time but their models are based on discrete-time measurements. Therefore, if sensitivity analysis is used as a tool supporting model development and evaluation of its quality, it should take this fact into account. Such models are usually very complex and include many parameters difficult to estimate in an experimental way. Changes of many of those parameters have little effect on model dynamics, and therefore they are called sloppy. In contrast, other parameters, when changed, lead to substantial changes in model responses and these are called stiff parameters. While this is a well-known fact, and there are methods to discern sloppy parameters from the stiff ones, they have not been utilized, so far, to create parameter rankings and quantify the influence of single parameter changes on system time responses. These single parameter changes are particularly important in analysis of signalling pathways, because they may pinpoint parameters, associated with the processes to be targeted at the molecular level in laboratory experiments. In the paper we present a new, original method of creating parameter rankings, based on an Hessian of a cost function which describes the fit of the model to a discrete experimental data. Its application is explained with simple dynamical systems, representing two typical dynamics exhibited by the signaling pathways.

3

Sensitivity analysis of deterministic signaling pathways models

Puszyński K., Lachor P., Kardyńska M., Śmieja J.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2012

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Vol. 60, nr 3

471-479

EN

The paper is focused on application of sensitivity methods to analysis of signaling pathway models. Two basic methods are compared: local, based on standard sensitivity functions, and global, based on Sobol indices. Firstly, a general outline of modeling of signaling pathways by means of ordinary differential equations is briefly described. Afterwards, the methods of sensitivity analysis, known from literature, are introduced and illustrated with a simple example of a dynamical system of the second order. Subsequently, the analysis of the p53/Mdm2 regulatory module, which is a key element of any pathway involving p53 protein, is presented. The results of this analysis suggest that no single method should be chosen for investigation of any signaling pathway model but several of them should be applied to answer important questions about sources of heterogeneity in cells behavior, robustness of signaling pathways and possible molecular drug targets.

4

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

Śmieja J.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 4

781-788

EN

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.

5

Model based analysis of signaling pathways

Śmieja J.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 2

139-145

EN

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.