A Detailed Study of the G-Protein Signalling Pathway
Using Exact Stochastic Reaction-Diffusion Simulations

Jerry E. Solomon
Center for Computational Biology
The Beckman Institute
California Institute of Technology
Pasadena, CA 91125

It is now widely recognized that traditional mass-action derived kinetic equationsare not suitable for modeling the biochemical reaction networks that drive intracellular behaviour. This approach assumes that the concentrations involved are large enough to be treated as continuous variables, that reaction rates are relatively fast, and that fluctuations can be ignored. These assumptions are almost never valid when treating intracellular reaction systems. Over the past several years, we have developed software tools which allow us to compute "exact" stochastic simulations of coupled biochemical reaction-diffusion systems. Such simulations are "exact" in the sense that they reproduce exactly the results one would obtain from solving the appropriate stochastic master equations describing the system.

One of the systems that we have been studying recently, using stochastic simulation, is the ubiquitous G-protein signaling system. The importance of this system arises from the fact that it is involved in a large number of developmental processes that require intercellular signaling coupled with intracellular responses. There are of course a number of distinct G-protein pathways that have been identified as cruciial in a variety of developmental processes. The specific G-protein pathway that we have chosen to study is one that begins with the activation of a G-protein complex by a particular agonist/receptor binding event, and ends with the release of large amounts of free Ca2+ from internal calcium stores maintained in the endoplasmic reticulum. Depending on context, this Ca2+ release event triggers various cellular responses to external signals.

An interesting aspect of this pathway, from a biochemistry standpoint, is the fact that most of its components undergoe two-dimensional diffusion on the inner surface of the cytoplasmic membrane. Thus, most of the reactions that constitute this pathway are diffusion-limited, with effective reaction rate coefficients that depend on the diffusion constants of the reacting partners. In applying our simulation approach to this problem, we first define the pathway explicitly in terms of the individual reaction events that make up the complete G-protein signaling pathway. In the case studied here, we have chosen the agonist/receptor pair to be the vertebrate versions of 'Wingless' (Wnt), and 'Frizzled' (Fz), as suggested from studies by Moon and collaborators. Of course, the simulation can handle any specific agonist/receptor pair that is appropriate to a particular intercellular signaling problem; one simply needs to modify the ligand- receptor binding/decay coefficients appropriately.

Once all of the reactions and associated parameters are specified our simulation code then "solves" this reaction system in order to provide a complete kinetic description of the behaviour of each of the molecular components of the pathway. As noted above, our stochastic simulation incorporates explicitly the fluctuations present in the system so we are able to see directly the effects (if any) of "noise" on the system.

The reaction rate coefficients and Michaelis-Menten thresholds were taken from the rather extensive literature on the G-protein system. Where such quatities were not available, we used estimates derived from previous experience on similar reactions. The simulation uses a total of 14 reaction channels, and their associated rate coefficients; in addition, there are three Michaelis-Menten coefficients, and three threshold constants used to complete the description of this pathway. The results that we obtained from our simulations were in good agreement with observations reported in the literature; in particular, the timing of major events, such as time to Ca2+ release from initial agonist/receptor binding, was found to be in good agreement with experimental observations. Since, aside from timing data, there are not many quantitative experimental measurements on the kinetic response curves of the signaling components, we can only report that the overall behaviour of the simulation is in good qualitative agreement with what is reported in the literature. Given these results, we believe that we now have a very good stochastic model of the G-protein pathway that can be used to study a variety of intercellular processes that utilize this pathway to accomplish various specific functions.

Several results of our simulations are shown in the figures below. The molecular concentrations are shown in units of (nM).

References

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©2001, California Institute of Technology. The material presented here may be used for NON-commercial purposes of research, publication, and presentation, provided adequate acknowledgement of the source is provided. No permission or license for commercial use is granted.