Time-Dependent Sensitivity Analysis of Biological Networks:  Coupled MAPK and PI3K Signal Transduction Pathways

Abstract

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.

Sensitivity analysis approaches applied to systems biology models

“…time-dependent response coefficient concentrations or rates at time t the parameter p j [29][30][31] …”

“…As the impact of model parameters on the model output changes over time, time-dependent parameter sensitivity analysis has been proposed to study the effect of parameter variation on model output at different time [29][30][31]. A parameter may have positive impact on the change of model output at early stage, but its effect can switch from positive to negative due to the complex feedbacks in the biological network.…”

Metabolic Control Analysis of Complex Biological Systems

“…For the systems that do not reach the steady-state, the control coefficients are defined by extending the definition of sensitivity functions to time-varying ones (Acerenza et al, 1989;Hu and Yuan, 2006). The coefficients are calculated by assuming that the response of a system is at the pseudosteady-state.…”

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

“…These indices provide information on which parameters are influential at particular times and can be integrated over time to identify those parameters which are most important in terms of the entire model output. This approach has been applied to a variety of biological systems [2,5,9,10]. However, by looking at individual time-points, we may miss interesting features in the model output.…”