Explaining a paradox and predicting behaviour:
A dynamical systems model of the G protein GTPase cycle
Benjamin Smith1, Claire Hill2, Louise Godfrey3, John Davey2 & Graham Ladds3
1MOAC
DTC, Coventry House, 2Biological Sciences, 3Warwick Medical School, Gibbet Hill Road, University of Warwick, Coventry, CV4 7AL
Biology
Mathematics
Combined Approach
GPCR Signalling
Simulating Experiments
Making Predictions
•G protein-coupled receptor (GPCR) signalling pathways
regulate diverse cellular processes (Hepler, 1999).
•The GTPase cycle of the G protein forms the central
signalling unit of these pathways.
•Regulator of G Protein Signalling (RGS) proteins regulate
the response (Ross and Wilkie, 2000).
•Model using a system of Ordinary Differential Equations.
•A range of different initial ligand conditions
→ simulate dose response.
•Altering parameter values and other initial conditions
→ simulate different strains.
•With a mathematical model, it is possible to manipulate
the system in any conceivable way.
•It is therefore possible to make predictions about how
the in vivo system will behave when the same
manipulations are applied.
•RGS proteins are important in both positive and negative
signal regulation.
Figure 1. Signalling through GPCRs.
Receptor activation promotes guanine
nucleotide exchange on Gα. “Active”
(GTP-bound)
Gα
produces
a
downstream
response through
effector molecules. RGS protein
“deactivates” Gα.
β γ
β γ
Gα
Gα
GDP
GTP
GTP autohydrolysis
GTP hydrolysis
RGS
Effector
Effector
Effector
RGS Proteins
•Accelerate GTP hydrolysis.
•Increase the “switching off” rate of GTP-bound Gα.
Hypothesis Development
•Initial models included rapid recycling by the RGS protein
(based on the model in Zhong et al., 2003).
•They were unable to reproduce GTPase enhanced
signalling.
•We’ve seen that permanently GTP-bound Gα cannot
produce maximal signalling.
•Postulate an “inert” GTP-bound state.
1 Gα-GTP can only activate 1 effector
molecule per round of signalling.
What happens when we remove RGS
protein from cells?
Response
Inert State
Effectoractive
Measuring Response
•The experimental system is the pheromone response
pathway in the yeast Schizosaccharomyces pombe.
•Response is measured using reporter genes.
•Cells are stimulated with increasing amounts of ligand to
generate dose response curves (Figure 2).
 GTP
Gα
RGS
Effectorinactive
What happens when we increase the
amount of RGS protein in cells?
•A prediction was made using the mathematical model
and the experiment was performed in vivo.
Simulation Data
600
400
300
200
0
B
RGS
RGS + Pi
RGSGαGTP
RGS
+ Pi
30
∆RGS
1xRGS
2xRGS
3xRGS
500
100
GαGTPEffector
 GTP
RGSGα
Biology Data
700
β -galactosidase activity
GPCR*
Response units
Ligand
-9
-8
-7
-6
-5
-4
25
∆Rgs1
1xRgs1
2xRgs1
3xRgs1
20
15
10
5
0
B
-9
-8
Log [Ligand] M
GαGDP
GαGTP
Activation
Figure 3. Schematic of the revised GTPase cycle hypothesis.
This is the central mechanism of the mathematical model.
-7
-6
-5
-4
Log [P factor] M
Figure 6. Predicting the effects of increasing RGS expression
in cells. Simulation predicts that doubling the amount of RGS
protein in cells reduces sensitivity and further increases maximal
signalling beyond wild-type levels. Trebling the amount of RGS is
predicted to further reduce sensitivity, but also to reduce maximal
signalling below that of wild-type. Results from in vivo assays show
good agreement with these predictions.
Conclusions
500
18
•RGS proteins reduce basal signalling but significantly
enhance maximal signalling.
RGS
∆RGS
Rgs1
∆Rgs1
400
16
Response Units
β -galactosidase activity
20
14
12
10
8
6
•Current understanding of GTPase cycle insufficient.
300
•Biological investigation of the “model” organism (Sz.
pombe) combined with computational investigation of a
mathematical model.
200
100
4
•A new state for the GTP-bound Gα is postulated.
2
-6
-5
-4
0
Basal
-9
-8
Explaining the paradox
• RGS proteins regulate signalling negatively and
positively.
•Their role in G protein recycling is already known to be
important (Doupnik et al., 1997).
•Is recycling alone sufficient to explain GTPase enhanced
signalling?
Biology Data
•The model was used to predict the effects of increasing
RGS expression.
•The GTPase accelerating effect of RGS proteins is
responsible for negative and positive regulation of
signalling through the Gα.
Future Work
•Perform parameter and principle component analysis.
Simulation Data
β -galactosidase activity
time
•Optimise parameters based upon a wide range of data.
500
40
35
30
25
0h
20
15
10
400
•Simulate a range of other strains and mutants.
300
200
100
5
0
0
B
-9
-8
-7
-6
-5
B
-4
-9
-8
-7
-6
-5
-4
Log[Ligand]
Log [P factor] M
35
30
25
4h
20
15
10
400
300
•Apply theory to other guanine nucleotide binding proteins
e.g. Ras, Rac, Rho.
200
100
5
0
0
B
-9
-8
-7
-6
-5
B
-4
-9
-8
-7
-6
-5
-4
Log[Ligand]
Log [P factor] M
References
500
40
35
30
25
8h
20
15
10
400
Doupnik,C.A., Davidson,N., Lester,H.A., and Kofuji,P. (1997). PNAS 94, 1046110466.
300
200
100
5
0
0
B
-9
-8
-7
-6
-5
B
-4
-9
-8
-7
-6
-5
-4
Log[Ligand]
Log [P factor] M
500
40
35
30
25
16h
20
15
10
Hepler,J.R. (1999). Trends Pharmacol. Sci. 20, 376-382.
Acknowledgements
300
200
100
0
-9
-8
-7
-6
Log [P factor] M
-5
-4
Zhong,H., Wade,S.M., Woolf,P.J., Linderman,J.J., Traynor,J.R., and Neubig,R.R.
(2003). J. Biol. Chem. 278, 7278-7284.
Ross,E.M. and Wilkie,T.M. (2000). Annu. Rev. Biochem. 69, 795-827.
400
5
0
•Extend the model to consider the effects of translocation
and post-translational modifications.
•Extend to include multiple receptor, G protein and RGS
species.
500
40
B
Can mathematical modelling help?
•Simulation of time-course and dose response data
shows good agreement with in vivo data.
-4
Time-course comparison
β -galactosidase activity
Maximum signalling is dependent upon
rapid GTP hydrolysis.
-5
•Comparing time-course data allows validation of model.
β -galactosidase activity
G protein Recycling
• Removing the RGS protein from cells would be expected
to increase signalling.
•Paradoxically, basal signalling is higher but maximal
signalling is lower (Figure 2).
•RGS insensitive mutant of Gα behaves like ∆Rgs1
→effects are due to the change in hydrolysis rate.
•Constitutively active mutant of Gα behaves like ∆Rgs1
→all Gα is GTP-bound but high levels of signalling are
never achieved.
•Gα turnover is necessary for high maximal response.
-6
Figure 4. Simulated dose response curves. The two strains from
Figure 2 were simulated: wild-type cells (RGS) and cells lacking an
RGS protein (∆RGS).
β -galactosidase activity
Figure 2. Biological dose response curves. Wild-type cells
(Rgs1), compared to that of cells lacking Rgs1 (∆Rgs1).
-7
Log[Ligand]
Response Units
-7
Log [P factor] M
Response Units
-8
Response Units
-9
Response Units
0
Basal
B
-9
-8
-7
-6
-5
-4
Log[Ligand]
Figure 5. Biological time-course vs. simulated time-course. A
comparison between the two shows good qualitative agreement.
•Dr Matthew Hodgkin (Biological Sciences, University of Warwick).
•Professor David Rand (Systems Biology DTC, University of
Warwick) .
•Molecular Organisation and Assembly in Cells (MOAC) DTC,
University of Warwick.