Bayesian Inference in Investigating Crosstalk Model for Calcium Signalling by GPCRs


The Original Study:

A Dual Receptor Crosstalk Model of G-Protein-Coupled Signal Transduction
P Flaherty, ML Radhakrishnan, T Dinh, RA Rebres, TI Roach, MI Jordan, AP Arkin.
2008. PLoS Computational Biology. 4(9) e1000185.


Summary

Crosstalk between G-proteins previously proposed:

1) Gβγ-exchange between Gαi-coupled and Gαq-coupled receptors, for enhanced GDP/GTP exchange relevant to receptor function (Quitterer & Lohse 1999); and

2) PLCβs regulated conditionally or dually Gβγs and Gα (Zhu & Birnbaumer 1996).


Statistical Inferences

The purpose of their inference was to observe posterior distribution over parameters for observable quantities (e.g. cytosolic calcium concentration) to determine degrees of certainty of hypotheses and to design new experiments accordingly.

Prior information was derived from in vitro and biochemical studies, as well as other experimental data; also employed was a model based on mass-action kinetics.


Biological System

Cells: RAW264.7 murine leukaemic monocyte derived macrophages

Ligands: C5a and uridine diphosphate (UDP)

Receptors:
C5aR (aka CD88) with possible effectors (Gi/0, β-arrestin1/2)
P2Y6 couples Gq/11
(P2Y14 with Gq/11: excluded in the model)

Signalling components included:
Gαi2, Gαq, Gβγ, PLCβ3, PLCβ4, PIP2, DAG, IP3, PKC, GRK2, calcium buffer, a Na2+/Ca2+ exchanger, a sarco(endo)plasmic reticulum Ca2+- ATPase (SERCA) pump, IP3Rs and RGS.


Model system

53 coupled ordinary differential equations with 84 parameters and 24 non-zero intial conditions. All the model equations, parameters and initial conditions are presented in supplementary materials.

20 of 84 parameters were estimated from cytosolic calcium measurements.

Only the two forward rate constants were estimated with data because of high degrees of correlation between forward and reverse rate constants in the posterior distribution, raising computational demand for Markov chain methods.

Each parameter was given an independent Gaussian prior on a log scale with a mean chosen from relevant literatures and a SD of 0.25.

The Metropolis-Hastings algorithm was used to estimate the posterior density of the parameters.

Three independent chains were simulated from different initial parameter values.

Convergence of the posterior distribution estimate was assessed by the Gelman-Rubin potential scale reduction factor (PSRF). Their multivariate PSFR was 2.44, individual PSRF was less than 1.5 (i.e. PSRF = 1 means converged distribution).

Predictive distribution was approximated by Monte Carlo sampling (details and equation in the method section of the original paper).


References

Flaherty P et al. 2008. A Dual Receptor Crosstalk Model of G-Protein-Coupled Signal Transduction. PLoS Computational Biology. 4: e1000185.

Quitterer U & Lohse M. 1999. Crosstalk between Gαi- and Gαq-coupled receptors is mediated by Gβγ exchange. Proc Natl Acad Sci U S A 96: 10626–10631.

Zhu X & Birnbaumer L. 1996. G protein subunits and the stimulation of phospholipase C by Gs- and Gi-coupled receptors: lack of receptor selectivity of Gα16 and evidence for a synergic interaction between Gβγ and the a subunit of a receptor activated G protein. Proc Natl Acad Sci U S A 93: 2827–2831