Hu Dawei, Yuan Jian-Min
Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104-2875, USA.
J Phys Chem A. 2006 Apr 27;110(16):5361-70. doi: 10.1021/jp0561975.
Sensitivity analysis has been widely used in the studies of complicated chemical reaction and biological networks, for example, in combustion studies and metabolic control analysis of pathways. In the latter cases, the responses of system properties at steady states with respect to changes of parameters, such as initial concentrations and rate constants, are often expressed as sensitivities. Besides steady-state sensitivities, time-dependent sensitivities should be useful; however, the explicit use of them in analyzing complicated biological systems has so far been limited. Using the coupled mitogen activated protein kinase (MAPK)-phophatidylinoisitol 3'-kinase (PI3K) system of the Ras pathways, known to be involved in about 30% of human cancers, as an example, we show that time-dependent sensitivities are useful for the studies of complex biological systems. They provide, for example, the following information: (a) multiple time scales existing in a complex system involving cross-talks and feedback loops; (b) the signs and strengths of responses to perturbations (as system complication increases, the signs of global responses are not always easily determined; for example, response may change sign more than once as time evolves); (c) beyond concentration dynamics, sensitivities revealing further details about the intricate dynamics and the effects of the cross-talks; (d) ranking of vulnerability of nodes of a biological network using integrated sensitivity-a first step toward the identification of drug targets; (e) reduced sensitivity serving as a measure of the stability or robustness of pathways. Our results indicate that the role of the PI3K branch in the coupled pathways is to enhance the robustness of the MAPK pathway. More importantly, they demonstrate that time-dependent sensitivity analysis can be a valuable tool in system biology.
敏感性分析已广泛应用于复杂化学反应和生物网络的研究中，例如在燃烧研究和代谢途径的控制分析中。在后一种情况下，稳态下系统性质相对于参数变化（如初始浓度和速率常数）的响应通常表示为敏感性。除了稳态敏感性外，时间相关的敏感性也应该是有用的；然而，到目前为止，它们在分析复杂生物系统中的明确应用还很有限。以已知与约30%的人类癌症相关的Ras途径的丝裂原活化蛋白激酶（MAPK）-磷脂酰肌醇3'-激酶（PI3K）耦合系统为例，我们表明时间相关的敏感性对于复杂生物系统的研究是有用的。例如，它们提供以下信息：（a）在涉及相互作用和反馈回路的复杂系统中存在多个时间尺度；（b）对扰动的响应的符号和强度（随着系统复杂性的增加，全局响应的符号并不总是容易确定；例如，响应可能会随着时间的推移不止一次地改变符号）；（c）除了浓度动态外，敏感性还揭示了关于复杂动态和相互作用影响的更多细节；（d）使用综合敏感性对生物网络节点的脆弱性进行排序——这是识别药物靶点的第一步；（e）降低的敏感性作为途径稳定性或鲁棒性的一种度量。我们的结果表明PI3K分支在耦合途径中的作用是增强MAPK途径的鲁棒性。更重要的是，它们证明了时间相关的敏感性分析可以成为系统生物学中的一个有价值的工具。
