(636d) Sensitivity Analysis of a Model of Calcium Dynamics Reveals Hot-Spots of Signaling

Given a computational model of a biochemical system in terms of its rate parameters, initial states and the equations, sensitivity analysis quantitatively characterizes the differential changes in the model outputs to perturbations in the parameters and initial states. Sensitivity analysis is a useful tool to study the relative ability of different components and conditions of a system to affect the overall behavior of the system. Sensitivity analyses can assist in optimal experiment design by identifying the parameters with respect to which the systems is more sensitive. Experiments should be designed for better identifiability of these parameters. Other ?less sensitive? parameters can be set to suitable values in appropriate range without much impact on the system outputs. Thus, sensitivity analysis has become an indispensable tool in quantitative analyses of biochemical systems. In recent years, both linear and nonlinear sensitivity analysis approaches have been applied to better understand biochemical systems such as signaling and metabolic pathways (1, 2). In our laboratory, we have used both linear and nonlinear direct and indirect approaches to compute or infer the sensitivity of several signaling pathways. Here we describe its application to a model of the dynamics of cytosolic calcium ions (Ca2+) in mouse macrophage RAW 264.7 cells in response to the anaphylatoxin complement 5a (C5a) (3-5).

Calcium is an important secondary messenger. Cytosolic Ca2+ affects many processes by regulating the activity of calmodulin and its downstream kinases. Specific to macrophage cells, calcium signaling is involved in the secretion of some of the cytokines and plays a role in phagocytosis. Elevated Calcium levels have been observed in macrophages in HIV encephalopathy, a brain disease leading to injury to the central nervous system (6). Thus, a detailed quantitative study of the regulation of Ca2+ is important. Recently we have developed a computational model for the regulation of [cytosolic Ca2+] accounting for the key upstream signaling pathways such as G-protein activation through G-protein coupled receptor (GPCR) and other regulators. Given the nonlinearity of the system, to comprehensively assess the effect of changes in the parameters and the important initial states, we have carried out two types of nonlinear sensitivity analysis: an indirect multiparametric variability analysis (MPVA) and direct single-parametric sensitivity analysis. Both the approaches are their results are described below.

In the indirect approach, also referred to as multiparametric variability analysis (MPVA) developed by Maurya et al. (7), the parameter-values obtained during the stochastic-search based optimization that fit the data well are analyzed. The parameters are sorted according to their decreasing range (ratio of the maximum to minimum value, MAX/MIN) across this good set of parameter-values. The system is less sensitive to the parameters with larger MAX/MIN or range. On the contrary, the system is more sensitive to the parameters with a narrow range (7). One potential drawback of this approach is that the MAX and MIN values can potentially depend on the lower bound (LB) and upper bound (UB) used in optimization and on the cutoff fit-error used to define the good sets. Hence, regular parametric sensitivity analysis is also carried out in which although only one parameter or initial state is perturbed at a time, both small and large perturbations are considered. Each parameter (one at a time) is perturbed by multiplying its base-value by factors [1/8 1/4 1/2 1 2 4 8]. After simulation, the shift in the basal-level (baseline-shift) and the peak-height compared to the respective basal-level are computed. Display of the differential changes has helped us glean out single-parametric nonlinear effects that would not have been possible otherwise. The broad results from both the approaches are common, viz., the total pool of Gβγ and GPCR kinase strongly affect the peak-height and basal levels. Essentially, G-protein signaling is very important. Another important module is the production of IP3. In the recent literature, Gβγ has been termed as a hot-spot of signaling and a target for drug-discovery (8). It interacts with many pathways and proteins. Different binding sites on Gβγ, e.g. for Gα, phospholipases, and GRK, may be selectively targeted by small molecules for therapeutic applications (9).

Key words: Calcium, intracellular signaling, sensitivity analysis, G beta gamma, macrophage, C5a.

References

1. Chu, Y., A. Jayaraman, and J. Hahn. 2007. Parameter sensitivity analysis of IL-6 signalling pathways. IET Syst Biol. 1:342-52.

2. Stephanopoulos, G., A. Aristidou, and J. Nielsen. 1998. Metabolic engineering: Principles and methodologies. Academic Press, San Diego, USA.

3. Maurya, M. R., and S. Subramaniam. 2007. A kinetic model for calcium dynamics in RAW 264.7 cells: 1. Mechanisms, parameters, and subpopulational variability. Biophys J. 93:709-28.

4. Maurya, M. R., and S. Subramaniam. 2007. A kinetic model for calcium dynamics in RAW 264.7 cells: 2. Knockdown response and long-term response. Biophys J. 93:729-40.

5. Maurya, M. R., and S. Subramaniam. 2007. Online Supporting material to: A kinetic model for calcium dynamics in RAW 264.7 cells: 1. Mechanisms, parameters, and subpopulational variability. Biophys J. 93:709-28.

6. Yi, Y. J., C. H. Lee, Q. H. Liu, B. D. Freedman, and R. G. Collman. 2004. Chemokine receptor utilization and macrophage signaling by human immunodeficiency virus type 1 gp120: Implications for neuropathogenesis. Journal Of Neurovirology. S10:91-96.

7. Maurya, M. R., S. J. Bornheimer, V. Venkatasubramanian, and S. Subramaniam. 2005. Reduced-order modeling of biochemical networks: Application to the GTPase-cycle signaling module. IEE Proc. - Systems Biology. 152:229-242.

8. Tesmer, J. J. 2006. Pharmacology. Hitting the hot spots of cell signaling cascades. Science. 312:377-8.

9. Bonacci, T. M., J. L. Mathews, C. Yuan, D. M. Lehmann, S. Malik, D. Wu, J. L. Font, J. M. Bidlack, and A. V. Smrcka. 2006. Differential targeting of Gbetagamma-subunit signaling with small molecules. Science. 312:443-6.