Kreutz Clemens, Raue Andreas, Timmer Jens
Physics Department, University of Freiburg, Hermann Herder Straße 3, 79104 Freiburg, Germany.
BMC Syst Biol. 2012 Sep 5;6:120. doi: 10.1186/1752-0509-6-120.
Predicting a system's behavior based on a mathematical model is a primary task in Systems Biology. If the model parameters are estimated from experimental data, the parameter uncertainty has to be translated into confidence intervals for model predictions. For dynamic models of biochemical networks, the nonlinearity in combination with the large number of parameters hampers the calculation of prediction confidence intervals and renders classical approaches as hardly feasible.
In this article reliable confidence intervals are calculated based on the prediction profile likelihood. Such prediction confidence intervals of the dynamic states can be utilized for a data-based observability analysis. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted.
The presented methodology allows the propagation of uncertainty from experimental to model predictions. Although presented in the context of ordinary differential equations, the concept is general and also applicable to other types of models. Matlab code which can be used as a template to implement the method is provided at http://www.fdmold.uni-freiburg.de/∼ckreutz/PPL.
基于数学模型预测系统行为是系统生物学的一项主要任务。如果从实验数据估计模型参数，则必须将参数不确定性转化为模型预测的置信区间。对于生化网络的动态模型，非线性与大量参数相结合阻碍了预测置信区间的计算，并使经典方法几乎不可行。
在本文中，基于预测轮廓似然性计算了可靠的置信区间。这种动态状态的预测置信区间可用于基于数据的可观测性分析。如果存在不可识别的参数，导致一些指定不充分的模型预测可解释为不可观测性，该方法也适用。此外，还引入了验证轮廓似然性，在解释有噪声的验证实验时应应用该似然性。
所提出的方法允许将不确定性从实验传播到模型预测。尽管是在常微分方程的背景下提出的，但该概念是通用的，也适用于其他类型的模型。可在http://www.fdmold.uni-freiburg.de/∼ckreutz/PPL获取用作实现该方法模板的Matlab代码。
