Probabilistic sensitivity analysis of biochemical reaction systems

Abstract

Sensitivity analysis is an indispensable tool for studying the robustness and fragility properties of biochemical reaction systems as well as for designing optimal approaches for selective perturbation and intervention. Deterministic sensitivity analysis techniques, using derivatives of the system response, have been extensively used in the literature. However, these techniques suffer from several drawbacks, which must be carefully considered before using them in problems of systems biology. We develop here a probabilistic approach to sensitivity analysis of biochemical reaction systems. The proposed technique employs a biophysically derived model for parameter fluctuations and, by using a recently suggested variance-based approach to sensitivity analysis ͓Saltelli et al., Chem. Rev. ͑Washington, D.C.͒ 105, 2811 ͑2005͔͒, it leads to a powerful sensitivity analysis methodology for biochemical reaction systems. The approach presented in this paper addresses many problems associated with derivative-based sensitivity analysis techniques. Most importantly, it produces thermodynamically consistent sensitivity analysis results, can easily accommodate appreciable parameter variations, and allows for systematic investigation of high-order interaction effects. By employing a computational model of the mitogen-activated protein kinase signaling cascade, we demonstrate that our approach is well suited for sensitivity analysis of biochemical reaction systems and can produce a wealth of information about the sensitivity properties of such systems. The price to be paid, however, is a substantial increase in computational complexity over derivative-based techniques, which must be effectively addressed in order to make the proposed approach to sensitivity analysis more practical.

Reducing experimental variability in variance-based sensitivity analysis of biochemical reaction systems

“…By following our previous work, 14 we consider a well-stirred (homogeneous) biochemical reaction system at a constant temperature and volume that consists of M coupled reactions:…”

“…These are most often taken to be published nominal values. 8,14,20 It turns out that different nominal values may produce different sensitivity results (see our example in Sec. VII), which can be very problematic in applications of the method to systems biology problems.…”

“…More specifically, we introduce two new sensitivity indices, which we refer to as noise-reduced variance-based sensitivity indices (NR-VSI's), that account for uncertainties in nominal reaction rate values due to experimental variability. Although these indices are a simple extension of the variance-based sensitivity indices considered in our previous work, 14 they are less sensitive to the choice of nominal rate values used and lead to a powerful sensitivity analysis methodology that can effectively accommodate appreciable levels of experimental variability.…”

“…[1][2][3][4] It has been extensively used to detect influential and noninfluential biochemical factors, [5][6][7] to simplify kinetic parameter estimation when designing genetic circuits, 8 to rank molecular species for system-based drug target selection, [9][10][11][12] and provide insights into system robustness and fragility. 13 In a previous paper, 14 we developed a thermodynamically consistent variance-based sensitivity analysis technique for investigating the effects of random biochemical factor fluctuations in a reaction system. This is a mathematically rigorous approach to sensitivity analysis that leads to a global understanding of the sensitivity properties of a biochemical reaction system by investigating the singular and joint effects of random parameter fluctuations on appropriately chosen system response characteristics.…”

“…14 Another important feature of our variance-based sensitivity analysis approach is that it can deal with three types of sensitivity analysis, namely, reaction-oriented sensitivity analysis (ROSA), species-oriented sensitivity analysis (SOSA), and reaction/species-oriented sensitivity analysis (ROSOSA). ROSA investigates the effect of fluctuations in the standard chemical potentials of the activated complexes of the reactions in a biochemical reaction system.…”