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Maurya et al. (2005), GTPase-Cycle Module

May 2008, model of the month by Michele Mattioni
Original model: BIOMD0000000085

Modeling big biochemical networks usually poses a big challenge from the modeling and computational point of view. It is, however, possible to use coarse-grained biochemical models, called reduced-orders model (ROMs), consisting of essential biochemical mechanisms, to study some properties of the network at less computational cost without losing the accuracy of the model.

Maurya et al ([1], BIOMD0000000085) have proposed a new approach to create ROMs, identifying potentially important parameters using multidimensional sensitivity analysis. One way to simplify a model is to use the classical sensitivity analysis that considers one parameter at time: If the parameter is not important for the output of the model it is excluded. However, this approach considers one parameter at a time, and interactions between parameters are not taken into account. The multiparametric variability analysis strategy (MPVA) can instead analyze the effect of simultaneous perturbation on several parameters, so that parametric interactions can be effectively taken into account and only parameters that do not influence other parameters are excluded. This is the approach used by the authors as a key feature of their framework. The algorithm used to reduce the complexity of a model is presented in Figure 1.

The estimation of the model parameters was done using a hybrid GA-based pseudo-global optimization. The constraint applied is to minimize the mismatch between the experimental data and the corresponding model prediction.

Reaction network for the detailed model of the GTPase-cycle module.

Figure 2: Reaction network for the detailed model of the GTPase-cycle module. Figure taken from [1].

Maurya et al have applied this approach to the GTPase-cycle module of m1 muscarin acetylcholine receptor, Gq, and regulator of G-protein signaling 4 (a GTPase-activating protein or GAP) starting from a detailed model of 48 reactions ([2], see Figure 2).

MPVA-based framework for model reduction

Figure 1: MPVA-based framework for model reduction. From [1]

Reduced model and results

Figure 3: (a) The reduced model is shown with bold arrows. Gray arrows represent the reactions present in the detailed model, excluded by the MVPA analysis. (b) Comparison of experimental data, data obtained by the original model and data simulated with the reduced model. (c) The four Limiting Signaling Regimes showing which are the rate limiting complexes.

One of the interesting outputs coming from the model is the fraction of active G-protein (Z)

Z = ([GT]+[RGT]+[RGAT]+[GAT])/([G]total)

where [G]total is the sum of the concentrations of all species involving G-protein; [GT] is the concentration of active G protein bound to GTP; [RGT] is the concentration of G protein bound to the complex of coupled receptor and GTP; [RGAT] is the concentration of G protein bound to the complex of coupled receptor, GTP and GAP; [GAT] is the concentration of G protein bound to the complex of GAP and GTP.

Figure 3 shows the use of this quantity to understand which are the Limiting Signaling Regimes (LSRs). The four Limiting Signaling Regimes arise by dominance of one of four kinetic paths represented by horizontal edges in Figure 2 (e.g.: G → GT → GD → G). The resulting simplified reaction network has only 17 reactions .

The model is able to replicate the detailed model and also suggests that the ternary complex between the G protein, the GTP-ase activating protein (GAP) and the receptor could be formed at once, instead of the classical mechanism where the inactive G protein binds to the receptor, exchanges GTP/GDP and then, in the active conformation, stimulates the downstream signaling pathway.

Bibliographic References

  1. M.R. Maurya, S.J. Bornheimer, V. Venkatasubramanian, and S. Subramaniam. Reduced-order modelling of biochemical networks: application to the GTPase-cycle signalling module. Systems Biology 152(4):229-242, 2005. [SRS@EBI]
  2. S.J. Bornheimer, M.R. Maurya, M.G. Farquhar, and S. Subramaniam. Computational modeling reveals how interplay between components of a GTPase-cycle module regulates signal transduction. Proc Natl Acad Sci U S A 101(45):15899-15904, 2004. [SRS@EBI]