Vera Julio, Rath Oliver, Balsa-Canto Eva, Banga Julio R, Kolch Walter, Wolkenhauer Olaf
Systems Biology and Bioinformatics Group, University of Rostock, 18051 Rostock, Germany.
Mol Biosyst. 2010 Nov;6(11):2174-91. doi: 10.1039/c0mb00018c. Epub 2010 Aug 18.
The investigation of the structure and dynamics of signal transduction systems through data-based mathematical models in ordinary differential equations or other paradigms has proven to be a successful approach in recent times. Extending this concept, we here analysed the use of kinetic models based on power-law terms with non-integer kinetic orders in the validation of hypotheses concerning regulatory structures in signalling systems. We integrated pre-existent biological knowledge, hypotheses and experimental quantitative data into a power-law model to validate the existence of certain regulatory loops in the Ras/Raf-1/MEK/ERK pathway, a MAPK pathway involved in the transduction of mitogenic and differentiation signals. Towards this end, samples of a human mammary epithelial cell line (MCF-10A) were used to obtain time-series data, characterising the behaviour of the system after epidermal growth factor stimulation in different scenarios of expression for the critical players of the system regarding the investigated loops (e.g., the inhibitory protein RKIP). The mathematical model was calibrated using a computational procedure that included: analysis of structural identifiability, global ranking of parameters to detect the most sensitivity ones towards the experimental setup, model calibration using global optimization methods to find the parameter values that better fit the data, and practical identifiability analysis to estimate the confidence in the estimated values for the parameters. The obtained model was used to perform computational simulations concerning the role of the investigated regulatory loops in the time response of the signalling pathway. Our findings suggest that the special regularity in the structure of the power-law terms make them suitable for a data-based validation of regulatory loops in signalling pathways. The model-based analysis performed identified RKIP as an actual inhibitor of the activation of the ERK pathway, but also suggested the existence of an intense feedback-loop control of the pathway by the activated ERK that maybe responsible for the damped oscillations we saw in the fraction of activated MEK both in the experiments and simulations. In addition, the model analysis suggested that phosphorylation/deactivation of RKIP during the transient stimulation may have a significant effect on the signalling peaks of both MEK and ERK. This later result suggests that dynamic modulation of signal inhibitors during stimulation may be a regulatory mechanism in ERK signalling and other pathways.
近年来，通过基于常微分方程或其他范式的基于数据的数学模型来研究信号转导系统的结构和动力学已被证明是一种成功的方法。扩展这一概念，我们在此分析了基于具有非整数动力学阶数的幂律项的动力学模型在验证信号系统调控结构相关假设中的应用。我们将已有的生物学知识、假设和实验定量数据整合到一个幂律模型中，以验证Ras/Raf-1/MEK/ERK信号通路（一种参与有丝分裂原和分化信号转导的MAPK信号通路）中某些调控环的存在。为此，使用人乳腺上皮细胞系（MCF-10A）的样本获取时间序列数据，以表征在不同表达情况下，该系统中与所研究环相关的关键参与者（如抑制蛋白RKIP）在表皮生长因子刺激后的行为。使用一种计算程序对数学模型进行校准，该程序包括：结构可识别性分析、参数的全局排序以检测对实验设置最敏感的参数、使用全局优化方法进行模型校准以找到最符合数据的参数值，以及实际可识别性分析以估计参数估计值的置信度。所获得的模型用于进行关于所研究调控环在信号通路时间响应中的作用的计算模拟。我们的研究结果表明，幂律项结构中的特殊规律性使其适用于基于数据的信号通路调控环验证。基于模型的分析确定RKIP是ERK通路激活的实际抑制剂，但也表明活化的ERK对该通路存在强烈的反馈环控制，这可能是我们在实验和模拟中观察到的活化MEK分数中出现阻尼振荡的原因。此外，模型分析表明，在瞬时刺激期间RKIP 的磷酸化/失活可能对MEK和ERK的信号峰有显著影响。这一结果表明，刺激期间信号抑制剂的动态调节可能是ERK信号通路和其他信号通路中的一种调控机制。
