| The network of Ras signaling pathways is known to be related to at least 30% of human cancers. In view of its importance, we investigate a mathematical model of the coupled mitogen activated protein kinase (MAPK)-phophatidylinoisitol 3'-kinase (PI3K) pathways, two better-known pathways of the Ras network. The objectives are to understand the dynamics, the effects of cross-talks, and design principles of these pathways using dynamic sensitivity analysis and non-equilibrium thermodynamics. Based on the knowledge gained in these analyses, we may be able to suggest means to control output signals.;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 MAPK and P13K pathways 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; (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---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 P13K 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 systems biology.;Thermodynamics is a branch of physics to treat macroscopic systems using a few variables. It would be interesting to use it to reduce the complexity of biochemical systems, such as signaling pathways. However, biological systems are usually not in equilibrium and are often far from equilibrium. To study such systems, we need nonequilibrium thermodynamics. Therefore, in the present work we have applied the modern concepts of non-equilibrium thermodynamics, such as, affinities, fluxes, dissipated energy, and efficiency to the studies of signaling pathways, in particular, the present coupled MAPK-P13K system. Motivated by the dynamics of these variables and using knowledge from sensitivity analysis, we can achieve certain degree of control of the output signals, which are related to cell growth and differentiation. |
