K. Fujarewicz, M. Kimmel, T. Lipniacki, and A. Świerniak (Poland)
Cell signaling pathways, nonlinear differential equations, parameter estimation
The dynamical behavior of a cell signaling pathway may be described by means of a set of nonlinear ordinary differential equations. Such a model involve parameters and frequently part of them are unknown. If the experimental data is available then parameters may be estimated. The key issue related to the problem of parameter estimation is the type of the data that most often comes from different blotting techniques. Two points are specially important. First, the data are collected only at discrete time moments that are relatively rare. Second, the data are only semi-quantitative, that means the values estimated based on blot images may be compared only within one blot and cannot be compared to data estimated based on other blots. To overcome the difficulties we propose an approach assuming existence of unknown multipliers (weights), one per one blot. Hence, the whole problem of fitting of the mathematical model depends on fitting not only parameters of the model but also the set of weights. In this paper we test the approach on NFκB transcription factor pathway.
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