Eriksson Olivia, Andersson Tom, Zhou Yishao, Tegnér Jesper
Division of Mathematical Statistics, Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.
BMC Syst Biol. 2011 Aug 7;5:123. doi: 10.1186/1752-0509-5-123.
One of the most well described cellular processes is the cell cycle, governing cell division. Mathematical models of this gene-protein network are therefore a good test case for assessing to what extent we can dissect the relationship between model parameters and system dynamics. Here we combine two strategies to enable an exploration of parameter space in relation to model output. A simplified, piecewise linear approximation of the original model is combined with a sensitivity analysis of the same system, to obtain and validate analytical expressions describing the dynamical role of different model parameters.
We considered two different output responses to parameter perturbations. One was qualitative and described whether the system was still working, i.e. whether there were oscillations. We call parameters that correspond to such qualitative change in system response essential. The other response pattern was quantitative and measured changes in cell size, corresponding to perturbations of modulatory parameters. Analytical predictions from the simplified model concerning the impact of different parameters were compared to a sensitivity analysis of the original model, thus evaluating the predictions from the simplified model. The comparison showed that the predictions on essential and modulatory parameters were satisfactory for small perturbations, but more discrepancies were seen for larger perturbations. Furthermore, for this particular cell cycle model, we found that most parameters were either essential or modulatory. Essential parameters required large perturbations for identification, whereas modulatory parameters were more easily identified with small perturbations. Finally, we used the simplified model to make predictions on critical combinations of parameter perturbations.
The parameter characterizations of the simplified model are in large consistent with the original model and the simplified model can give predictions on critical combinations of parameter perturbations. We believe that the distinction between essential and modulatory perturbation responses will be of use for sensitivity analysis, and in discussions of robustness and during the model simplification process.
细胞周期是描述最为详尽的细胞过程之一，它调控着细胞分裂。因此，这个基因 - 蛋白质网络的数学模型是一个很好的测试案例，可用于评估我们在多大程度上能够剖析模型参数与系统动态之间的关系。在这里，我们结合两种策略来探索与模型输出相关的参数空间。将原始模型的简化分段线性近似与同一系统的敏感性分析相结合，以获得并验证描述不同模型参数动态作用的解析表达式。
我们考虑了对参数扰动的两种不同输出响应。一种是定性的，描述系统是否仍在运行，即是否存在振荡。我们将对应于系统响应这种定性变化的参数称为关键参数。另一种响应模式是定量的，测量细胞大小的变化，这对应于调节参数的扰动。将简化模型关于不同参数影响的解析预测与原始模型的敏感性分析进行比较，从而评估简化模型的预测。比较结果表明，对于小扰动，关于关键参数和调节参数的预测是令人满意的，但对于较大扰动，差异更为明显。此外，对于这个特定的细胞周期模型，我们发现大多数参数要么是关键参数，要么是调节参数。关键参数需要较大扰动才能识别，而调节参数通过小扰动更容易识别。最后，我们使用简化模型对参数扰动的关键组合进行预测。
简化模型的参数特征在很大程度上与原始模型一致，并且简化模型可以对参数扰动的关键组合进行预测。我们相信，关键扰动响应和调节扰动响应之间的区别将有助于敏感性分析，以及在稳健性讨论和模型简化过程中发挥作用。
