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Analysis Procedure for Signal Transduction Pathways by Clustering Parameters According to Their Sensitivity Profiles

Yunfei Chu, Zuyi (Jacky) Huang, and Juergen Hahn. Department of Chemical Engineering, Texas A& M University, College Station, TX 77843-3122

Analysis procedure for signal transduction pathways by clustering parameters according to their sensitivity profiles

Mathematical modeling and analysis of signal transduction networks plays an important role in systems biology. Models of signal transduction networks generally consist of nonlinear differential equations (Schoeberl et al., 2002; Singh et al., 2006) with a large number of parameters whose values are not precisely known and only a portion of which can be estimated from experimental data.

Sensitivity analysis techniques are commonly used to determine the key parameters of a model. Sensitivity values are used to rank the importance of the effect of changes in parameter values on the output. However, for a dynamic system the sensitivity is a function of time and lumping the effect over time into a scalar value only provides partial information about the importance of a parameter. One reason for this is that parameters which have similar cumulative effects may still cause very different dynamic changes of the outputs. It has been recognized that distinct temporal activation profiles of the same signaling proteins result in diverse physiological responses (Marshall, 1995; Hoffmann et al., 2002; Kholodenko 2006) and, therefore, categorizing the dynamic effects of parameters is of great importance.

The aim of this work is to use the entire time-dependent sensitivity profile of parameters for ranking the importance of parameters of signal transduction networks but also to determine which parameters have similar dynamic sensitivity profiles that cannot be distinguished from one another. A technique based on parameter clustering of the sensitivity profiles is developed to rank the parameters. A similarity measure is defined to quantify correlations among the effects that changes in parameters have on the measurements. If the similarity measure has a value of unity then the effects of two parameters cannot be distinguished from one another, i.e., the effect caused by changes in one of the parameters can be compensated by changing the other one. If the similarity is zero then the two parameters have distinct effects. The parameters can be grouped by a clustering algorithm based upon their sensitivity profile. Since parameters in a group have correlated effects, the magnitude of the sensitivity vector can be used to rank the parameters in a group. The parameter with the longest sensitivity vector in each group can be selected as the representative parameter of that group. Thus, the technique identifies the important parameters of the signal transduction network as the representative parameters for each of the groups.

The advantage of this technique over conventional methods is that the parameters are ranked by their dynamic effects rather than the cumulative effects only. This allows to not only determine a set of parameters that are important for the signal transduction network but also to characterize the effect that changes in parameters have on the output. As a result it is possible to view each cluster of parameters as a set of parameters where uncertainty in the value of any of the parameters can be compensated by the values of other parameters. For illustration purposes this technique is applied to the Jak/STAT and MAPK/NF-IL-6 signal transduction network stimulated by interleukin 6.


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