### Data Set

The time interval between samples is approximately 3-4 seconds and each
time series is approximately 100-300 seconds of post-stimulation data.
Table 1 shows a summary of the knockdown data used for statistical
parameter estimation for this model in addition to the wild-type
experiments.

<table>
<colgroup>
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 0%" />
<col style="width: 10%" />
<col style="width: 7%" />
<col style="width: 6%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 10%" />
<col style="width: 8%" />
</colgroup>
<tbody>
<tr class="odd">
<td> </td>
<td><strong> </strong></td>
<td colspan="2"><strong> </strong></td>
<td><strong> </strong></td>
<td><strong> </strong></td>
<td><strong> </strong></td>
<td colspan="6"><strong>Sample Size</strong></td>
</tr>
<tr class="even">
<td></td>
<td colspan="3"><strong>Measured Fraction Knockdown</strong></td>
<td colspan="3"><strong>Model Value</strong></td>
<td colspan="3"><strong>C5a</strong></td>
<td colspan="3"><strong>UDP</strong></td>
</tr>
<tr class="odd">
<td>Cell Line</td>
<td colspan="2">qRT-PCR</td>
<td>Western</td>
<td>Nominal</td>
<td>Lower</td>
<td>Upper</td>
<td>&lt;10nM</td>
<td>10 - 100nM</td>
<td>&gt;100nM</td>
<td>&lt;1μM</td>
<td><p>1 –</p>
<p>10μM</p></td>
<td>&gt; 10μM</td>
</tr>
<tr class="even">
<td>Wild-type</td>
<td colspan="2">-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>4</td>
<td>8</td>
<td>3</td>
<td>5</td>
<td>5</td>
<td>4</td>
</tr>
<tr class="odd">
<td>GRK2 (2)</td>
<td colspan="2">90% ± 7%, n=5</td>
<td>40% ± 6%, n=6</td>
<td>40.0%</td>
<td>22.0%</td>
<td>58.0%</td>
<td>2</td>
<td>12</td>
<td>2</td>
<td>3</td>
<td>1</td>
<td>5</td>
</tr>
<tr class="even">
<td>Gai2 (3)</td>
<td colspan="2">83% ± 5%, n=4</td>
<td>73% ± 6%, n=5</td>
<td>73.0%</td>
<td>55.0%</td>
<td>91.0%</td>
<td>-</td>
<td>5</td>
<td>-</td>
<td>5</td>
<td>-</td>
<td>7</td>
</tr>
<tr class="odd">
<td>Gaq (3)</td>
<td colspan="2">70% ± 8%, n=7</td>
<td>66% ± 23%, n=2</td>
<td>66.0%</td>
<td>0.0%</td>
<td>95.0%</td>
<td>-</td>
<td>3</td>
<td>-</td>
<td>1</td>
<td>-</td>
<td>3</td>
</tr>
<tr class="even">
<td>PLCb3 (1)</td>
<td colspan="2">-</td>
<td>83% ± 15%, n=3</td>
<td>83.0%</td>
<td>38.0%</td>
<td>100.0%</td>
<td>-</td>
<td>3</td>
<td>-</td>
<td>-</td>
<td>-</td>
<td>3</td>
</tr>
<tr class="odd">
<td>PLCb4 (1)</td>
<td colspan="2">87% ± 6%, n=5</td>
<td>-</td>
<td>87.0%</td>
<td>69.0%</td>
<td>100.0%</td>
<td>-</td>
<td>4</td>
<td>-</td>
<td>4</td>
<td>-</td>
<td>4</td>
</tr>
</tbody>
</table>

Table 1: The data set used for parameter estimation is shown in this
table. Five different cell lines which have a perturbation in the level
of a key signal transduction protein were constructed by shRNAi
lentiviral infection. The calcium response from these cell lines in
addition to the wild-type cell line were used to fit relevant parameters
in the model. Since shRNAi does not entirely remove the protein product,
the fraction knockdown was estimated by qRT-PCR and by Western blot
analysis. The standard error (se) was computed for each estimate and the
upper and lower confidence intervals were computed as ±3·se. The
knockdown confidence intervals are used in the GPCR model to construct
prediction confidence intervals for the calcium response. Where several
cell lines were constructed for each knockdown, the best was selected
and reported in parenthesis. The sample size for each knockdown-ligand
dose combination is shown in the last 6 columns.

This data set was first used to check the accuracy of the model. The
five knockdown perturbations and the range of ligand doses impose strong
quantitative constraints on the model.

### 

### Model & Data Preprocessing

From the vantage point of an average cell, the concentration of ligand
is at first zero, then as the ligand molecules diffuse in the media the
effective concentration at the membrane interface asymptotes to the
equilibrium concentration. We employ the following model for the ligand
concentration at the plasma membrane interface as a function of time

![](media/image1.wmf)

and fit parameters of the model using FITC measurements as described in
the supplementary information. Figure S5 shows the fit of the model to
the FITC data.

Fura-2 measurements report only the relative change in cytosolic calcium
and are not able to report absolute calcium levels. In order that the
baseline concentration of cytosolic calcium in our model match a
reasonable resting cytosolic calcium concentration we subtracted the
average the prestimulus calcium concentration for each experiment and
recentered the baseline at 80nM which is a reasonable physiological
level for these cells.

In our model we have lumped PLCβ2 and PLCβ3 because their regulators and
effectors in the context of the rest of the calcium model are identical.
However, the experimental perturbations of PLCβ3 left PLCβ2
concentrations unchanged. Accordingly, we took the knockdown fraction to
be 50% of that reported by western blot analysis for the purposes of
simulation of PLCβ3 knockdown experiments.

## Detailed Statistical Inference

Twenty of the 84 parameters were chosen to be estimated from data based
on relevance to the experimental data. Only those parameters that
related to the knockdown experiments in the data set were estimated and
are denoted with a star in Table S2. We used data to estimate only the
two forward rate constants in the enzymatic mass-action equations
because the forward and reverse rate constants for a given reaction will
be highly correlated in the posterior distribution making estimation by
Markov chain methods computationally expensive.

For each estimated parameter we constructed an independent Gaussian
prior on a log scale with a mean chosen based on relevant literature and
a standard deviation of 0.25. We found that this prior variance was
sufficiently permissive to the exploration of the space while still
constraining the rates to be physically reasonable. The prior
distribution over the parameters allows the incorporation of both soft
and hard constraints in the parameter estimates. Parameter sets with
zero measure are not permitted in the posterior distribution and
parameter sets with small measure must be assigned a large likelihood in
order to have a large posterior probability.

The likelihood function links the prior distribution with the posterior
distribution under Bayes rule

![](media/image2.wmf).

In our model, the likelihood function is a Gaussian distribution
according to the non-linear regression equation![](media/image3.wmf),
where ![](media/image4.wmf) is the deterministic model prediction. The
posterior distribution is of interest because it informs us as to the
most probable setting of the parameters as well as the uncertainty in
the values.

The Metropolis-Hastings algorithm (1) was used to estimate the posterior
density of the parameters Pr(θ\|**y**) . Since the posterior density of
the parameters has significant correlation structure, three independent
chains were simulated from different initial parameter values. Each
chain was simulated for a burn-in period of 50,000 iterations and then a
sample size of 29906 was taken with a thinning factor of 10. To assess
convergence of the posterior distribution estimate, we used the
Gelman-Rubin potential scale reduction factor (PSRF) (2). The
multivariate PSRF is 2.44 and 95% of the individual PSRFs were less than
1.5. A PSRF value of one indicates that the distribution has converged
and values near one are close to converged.

Posterior prediction confidence intervals were constructed using the
percentiles from the predictive distribution approximated with 2000
Monte Carlo samples from ![](media/image5.wmf) at each of 100 simple
random samples from ![](media/image6.wmf) according to

![](media/image7.wmf)

where ![](media/image8.wmf) and ![](media/image9.wmf) is the pooled
variance estimate, which is computed as an average of the variances of
all the time points in each of the 29 wild-type experiments. These
average variances are weighted by the number of technical replicates in
each experiment and then averaged to yield the estimate
![](media/image10.wmf).

The observed standard deviation for each calcium measurement was
obtained from 3-4 replicates on the same plate. By chance the replicate
measurements for some time points were nearly identical causing the
standard deviation estimate to be close to zero. Since the log of the
likelihood for a Gaussian distribution contains the standard deviation
estimate in the denominator, a near-zero value will force the likelihood
to be very large unless a parameter value is selected which causes the
simulation value to be very close to the measured value in the
numerator. This effectively causes only a few terms in the likelihood to
have a disproportionate importance in the model fit. We implemented a
common remedy for this situation. A small constant factor (1nM) was
added to the estimate of the standard deviation.

Figure S1:

This figure shows exemplar MCMC realizations for parameter k109f (the
UDP+P2YR forward binding rate) from three independent chains. The chains
have converged to the stationary distribution which is the posterior
distribution as measured by the PSRF (see Materials and Methods).

![](media/image11.png){width="6.000694444444444in" height="5.54375in"}

Figure S2: Posterior Distributions & Correlations

The first figure shows that the pairwise marginal posterior
distributions for the ligand binding reactions for P2YR and C5aR. The
posterior distributions show the dissociation constants for the
reactions are tightly constrained by the data, while the values of the
forward and reverse rates that make up the ratio are not as well
constrained by the data. Additionally, the UDP binding rates are not
correlated with the C5a binding rates. k108f and k108r are the P2YR
forward and reverse rates and k101f and k101r are the C5aR rates.

The next two figures show the one-way marginal posterior density
estimates from three independent MCMC chains with approximately 30,000
samples. The 20 estimates parameters are along the rows and the
independent chains are along the columns. In each plot, the light blue
density is the prior density and the green, purple and orange densities
are the posterior densities. The vertical line shows the parameter value
used in the model simulations in the paper and listed in table S3. All
of the densities are plotted on a log scale.

Each marginal posterior distribution estimate is constructed from
independent MCMC chains. The results from each chain (three of them) are
shown in the columns of the second figure below. In some cases the
algorithm sampled heavily from one mode that was not explored as heavily
by another chain. However, the PSRF criterion used to assay convergence
and a visual inspection of overall posterior density correspondence do
indicate that the posterior distributions are sufficiently sampled by
all three chains in aggregate. Furthermore, the fit of the model to the
data as shown in figure S3 shows that the model point estimates are
effective in fitting the actual calcium measurements.

![](media/image12.png){width="5.990277777777778in" height="5.98125in"}

![](media/image13.png){width="3.8361111111111112in" height="9.6in"}

![](media/image14.png){width="3.8361111111111112in" height="9.6in"}

Figure S3: Peak Height Dose Response

This figure shows the single ligand calcium dose responses for C5a and
UDP stimulation.

![](media/image15.png){width="5.510416666666667in"
height="4.248611111111111in"}

![](media/image16.png){width="5.488888888888889in"
height="4.248611111111111in"}

Figure S4: Knockdown Simulations

This figure shows representative simulations and data for each knockdown
experiment. A complete set of all 96 experiments is provided in a
supplementary folder.

+---+---------------------------------+--------------------------------+
|   | C5a                             | UDP                            |
+---+---------------------------------+--------------------------------+
| > | 250nM                           | 25μM                           |
|   |                                 |                                |
| W | ![](media/image17.p             | ![](media/image18.png          |
| i | ng){width="2.859027777777778in" | ){width="2.8152777777777778in" |
| l | height="1.6in"}                 | height="1.6in"}                |
| d |                                 |                                |
| - |                                 |                                |
| t |                                 |                                |
| y |                                 |                                |
| p |                                 |                                |
| e |                                 |                                |
+---+---------------------------------+--------------------------------+
| > | 250nM                           | 25μM                           |
|   |                                 |                                |
| G | ![](media/image19.pn            | ![](media/image20.png          |
| R | g){width="2.7381944444444444in" | ){width="2.8041666666666667in" |
| K | height="1.6in"}                 | height="1.6in"}                |
| 2 |                                 |                                |
+---+---------------------------------+--------------------------------+
| > | 100nM                           | 25μM                           |
|   |                                 |                                |
| G | ![](media/image21.p             | ![](media/image22.png          |
| α | ng){width="2.848611111111111in" | ){width="2.7604166666666665in" |
| i | height="1.6in"}                 | height="1.6in"}                |
| 2 |                                 |                                |
+---+---------------------------------+--------------------------------+
| > | 100nM                           | 25μM                           |
|   |                                 |                                |
| G | ![](media/image23.pn            | ![](media/image24.png          |
| α | g){width="2.7604166666666665in" | ){width="2.7604166666666665in" |
| q | height="1.6in"}                 | height="1.6in"}                |
+---+---------------------------------+--------------------------------+
| > | 100nM                           | 25μM                           |
|   |                                 |                                |
| P | ![](media/image25.pn            | ![](media/image26.png          |
| L | g){width="2.7930555555555556in" | ){width="2.7381944444444444in" |
| C | height="1.6in"}                 | height="1.6in"}                |
| β |                                 |                                |
| 3 |                                 |                                |
+---+---------------------------------+--------------------------------+
| > | 30nM                            | 25μM                           |
|   |                                 |                                |
| P | ![](media/image27.pn            | ![](media/image28.png          |
| L | g){width="2.7930555555555556in" | ){width="2.8152777777777778in" |
| C | height="1.6in"}                 | height="1.6in"}                |
| β |                                 |                                |
| 4 |                                 |                                |
+---+---------------------------------+--------------------------------+

Figure S5: Input Model Fit

This figure shows the input model (described in Materials and Methods)
fit to the FITC measurements. The ligand concentration that the cell
sees does not transit instantaneously from 0 to the final concentration.
The ligand concentration is expected to take an amount of time that is
significant on the scale of the measurements made for this study to
reach the final concentration.

![](media/image29.png){width="3.5104166666666665in"
height="3.079861111111111in"}

Figure S6: Large Pathway Diagram

![](media/image30.png){width="7.489583333333333in" height="5.7875in"}

Figure S7: System of Differential Equations

This figure shows the complete set of differential equations used to
simulate the model. These equations are also available in the source c
code for the model supplied. This system of equations with the initial
conditions and nominal parameter values reported in Tables S1 and S2
respectively completely define the model and allow for the reproduction
of the simulations used in this paper on any platform.

![](media/image31.png){width="5.892361111111111in"
height="7.286111111111111in"}

![](media/image32.png){width="5.975in" height="7.522916666666666in"}

![](media/image33.png){width="5.9534722222222225in" height="5.5125in"}

Figure S8: Hill function self-synergy. Consider a Hill function,
$H(x) = \frac{x^{n}}{x^{n} + K^{n}}$. $y \ast \frac{x \ast}{K}$is a
dimensionless critical concentration $y \ast$ , below which self-synergy
will occur. Based on the analysis, we conclude that: (i) *n* must be
greater than 1 for self-synergy to occur, (ii) self synergy never occurs
if the concentration *x* exceeds equilibrium constant *K* (y \> 1), and
(iii) for *n \> 2*, there is a large range of concentration for
self-synergy. In the G protein model, x, is the concentration of
IP3-IP3R, H(x) is the rate of change in cytosolic calcium concentration
and n=4.

We have tested the validity of this self synergy hypothesis by
stimulating the cells with both 20nM UDP and 40nM UDP (data not shown).
Though at such low ligand concentrations, the measurement variability is
high, we observed that the synergy ratio, on average was 1.17 compared
to a value of 1.25 predicted by the model.

![](media/image34.wmf){width="3.998611111111111in"
height="3.2284722222222224in"}

Figure S9: Parameter Sensitivity Analysis. The parameter of interest is
varied by 10% while all other parameters are kept constant. The
parameters are grouped according to their functionalities. The
sensitivity coefficient is the ratio of the relative change in the peak
height to the relative change in the parameter value. The four most
sensitive parameters (sensitivity coefficient \> 2) in the Ca~cyt~
category are Vqssk50 (IP3+IP3K_a -\> IP4+IP3K_a (Vmax)), Kqssk50
(IP3+IP3K_a -\> IP4+IP3K_a (Km)), a1 (Ca leak into the cell from
outside), and Kex (Na/Ca exchange activation const). The top 3 most
sensitive parameters in the PLCb3 category are: k21bf\*
(PLCb3_Ca_Gbg_PIP2 -\> PLCb3_Ca_Gbg+IP3+DAG), k20f (Gbg+PLCb3_Ca -\>
PLCb3_Ca_Gbg), k21af\* (PLCb3_Ca_Gbg+PIP2 -\> PLCb3_Ca_Gbg_PIP2). A star
next to the parameter name indicates it was estimated.

![](media/image35.png){width="6.549305555555556in"
height="3.9090277777777778in"}

Table S1: Model Initial Conditions

This table shows the initial conditions used for the model. The model
was run for sufficient time for the species states in the model to reach
equilibrium before ligand stimulation was added. The number of molecules
was calculated using a cell volume of 1pL.

  -------------- ----------- --------------- -----------------------------------
  **Name**       **Initial   **Molecules**   **Description**
                 Value                       
                 (μM)**                      

  c5aR           5.00E-02    30100           C5a receptor concentration

  p2yr           1.00E-01    60200           P2Y receptor concentration

  Gβγ            7.14E+00    4299990         Gβγ concentration

  Gαi_GDP        6.64E+00    3999989         Gαi concentration

  Gαq_GDP        4.98E-01    300001          Gαq concentration

  PLCβ3          1.16E-01    70001           PLCβ3 concentration

  PLCβ4          6.64E-02    40000           PLCβ4 concentration

  PIP2           5.00E-01    301000          

  IP3            1.80E-03    1084            Free IP3 concentration

  DAG            1.00E-03    602             Free DAG concentration

  IP3R           2.08E-02    12492           IP3 receptor concentration

  IP3R-IP3       1.75E-03    1054            

  IP3R-IP3-Ca    2.30E-03    1385             

  IP3R-Ca        2.00E-04    120             

  Ca             7.86E-02    47317           Cytosolic Calcium concentration

  CaER           1.04E+01    6231302         IP3 sensitive stored calcium
                                             concentration

  PKC            2.49E-02    15000            

  GRK            2.31E-02    13880           GRK concentration

  RGS_a          2.31E-02    13880           Regulator of G protein Signaling

  Buf            4.50E-01    270599          

  CaBuf          5.05E-02    30401            

  IP3K_a         1.66E-03    1000            

  IP4            1.00E-01    60200            

  IP5            1.00E-01    60200            
  -------------- ----------- --------------- -----------------------------------

Table S2: Model Parameters

This table shows the nominal parameters used for the model. Parameter
distributions that were estimated are shown as shaded rows and with a
star next to the parameter name in the table. The prior distribution for
each parameter is as described in the Materials and Methods section with
mean value specified by the column labeled \"prior\".

  ----------------------------------------------------------------------------------------
  **Constant**   **Prior**   **Nominal**   **Unit**   **Description**
  -------------- ----------- ------------- ---------- ------------------------------------
  k108f\*        1.628       13.20         μM-1 s-1   UDP+p2yr -\> UDPC

  k108r\*        0.165       3.61          s-1        UDP+p2yr \<- UDPC

  k101f\*        12.143      92.41         μM-1 s-1   c5a+c5aR -\> c5aC

  k101r\*        0.0378      0.376         s-1        c5a+c5aR \<- c5aC

  k102af         591.54      591.54        μM-1s-1    GRKp_Gbg+c5aC -\> GRKp_Gbg_c5aC

  k102ar         12.367      12.36         s-1        GRKp_Gbg+c5aC \<- GRKp_Gbg_c5aC

  k102bf\*       123.31      199.31        s-1        GRKp_Gbg_c5aC -\> GRKp_Gbg+c5aCp

  k104f          0.0001      0.0001        s-1        c5aCp -\> c5aR+c5a

  k105f\*        0.0945      0.012         μM-1 s-1   c5aC+Gbg_Gai_GDP -\>
                                                      c5aC+Gbg+Gai_GTP

  k106f          0.0222      0.0222        s-1        Gai_GTP -\> Gai_GDP

  k109f\*        0.2686      0.137         μM-1 s-1   UDPC+Gbg_Gaq_GDP -\>
                                                      UDPC+Gbg+Gaq_GTP

  k110f          0.0222      0.0222        s-1        Gaq_GTP -\> Gaq_GDP

  k11f           7000        7000          μM-1 s-1   Gai_GDP+Gbg -\> Gbg_Gai_GDP

  k113f          7000        7000          μM-1 s-1   Gaq_GDP+Gbg -\> Gbg_Gaq_GDP

  k9af           100         100           μM-1 s-1   RGS_a+Gai_GTP -\> RGS_a_Gai_GTP

  k9ar           0.1         0.1           s-1        RGS_a+Gai_GTP \<- RGS_a_Gai_GTP

  k9bf           100         100           s-1        RGS_a_Gai_GTP -\> RGS_a+Gai_GDP

  k111af         100         100           μM-1 s-1   RGS_a+Gaq_GTP -\> RGS_a_Gaq_GTP

  k111ar         0.1         0.1           s-1        RGS_a+Gaq_GTP \<- RGS_a_Gaq_GTP

  k111bf         100         100           s-1        RGS_a_Gaq_GTP -\> RGS_a+Gaq_GDP

  k12f           20          20            μM-1 s-1   PLCb4+Ca -\> PLCb4_Ca

  k12r           8           8             s-1        PLCb4+Ca \<- PLCb4_Ca

  k13f           62.55       62.55         μM-1 s-1   PLCb4_Ca+Gaq_GTP -\>
                                                      PLCb4_Ca_Gaq_GTP

  k13r           10.632      10.63         s-1        PLCb4_Ca+Gaq_GTP \<-
                                                      PLCb4_Ca_Gaq_GTP

  k15af\*        100         1238.78       μM-1 s-1   PLCb4_Ca_Gaq_GTP+PIP2 -\>
                                                      PLCb4_Ca_Gaq_GTP_PIP2

  k15ar          1           1             s-1        PLCb4_Ca_Gaq_GTP+PIP2 \<-
                                                      PLCb4_Ca_Gaq_GTP_PIP2

  k15bf\*        3           22.85         s-1        PLCb4_Ca_Gaq_GTP_PIP2 -\>
                                                      PLCb4_Ca+Gaq_GDP+IP3+DAG

  k16f           20          20            μM-1 s-1   PLCb3+Ca -\> PLCb3_Ca

  k16r           8           8             s-1        PLCb3+Ca \<- PLCb3_Ca

  k17f           50          50            μM-1 s-1   PLCb3_Ca+Gaq_GTP -\>
                                                      PLCb3_Ca_Gaq_GTP

  k17r           0.1         0.1           s-1        PLCb3_Ca+Gaq_GTP \<-
                                                      PLCb3_Ca_Gaq_GTP

  k19af\*        100         70.87         μM-1 s-1   PLCb3_Ca_Gaq_GTP+PIP2 -\>
                                                      PLCb3_Ca_Gaq_GTP_PIP2

  k19ar          1           1             s-1        PLCb3_Ca_Gaq_GTP+PIP2 \<-
                                                      PLCb3_Ca_Gaq_GTP_PIP2

  k19bf\*        3           27.89         s-1        PLCb3_Ca_Gaq_GTP_PIP2 -\>
                                                      PLCb3_Ca+Gaq_GDP+IP3+DAG

  k20f           8.346       8.346         μM-1 s-1   Gbg+PLCb3_Ca -\> PLCb3_Ca_Gbg

  k20r           0.388       0.388         s-1        Gbg+PLCb3_Ca \<- PLCb3_Ca_Gbg

  k21af\*        80          165.83        μM-1 s-1   PLCb3_Ca_Gbg+PIP2 -\>
                                                      PLCb3_Ca_Gbg_PIP2

  k21ar          8           8             s-1        PLCb3_Ca_Gbg+PIP2 \<-
                                                      PLCb3_Ca_Gbg_PIP2

  k21bf\*        1           5.41          s-1        PLCb3_Ca_Gbg_PIP2 -\>
                                                      PLCb3_Ca_Gbg+IP3+DAG

  k24af          10          5.89          μM-1 s-1   PKC_DAG_Ca+PLCb4_Ca -\>
                                                      PKC_DAG_Ca_PLCb4_Ca

  k24ar          11          11            s-1        PKC_DAG_Ca+PLCb4_Ca \<-
                                                      PKC_DAG_Ca_PLCb4_Ca

  k24bf          1           0.93          s-1        PKC_DAG_Ca_PLCb4_Ca -\>
                                                      PKC_DAG_Ca+PLCb4_Ca_p

  k25af          110         830.44        μM-1 s-1   PKC_DAG_Ca+PLCb3_Ca -\>
                                                      PKC_DAG_Ca_PLCb3_Ca

  k25ar          11          11            s-1        PKC_DAG_Ca+PLCb3_Ca \<-
                                                      PKC_DAG_Ca_PLCb3_Ca

  k25bf          1           11.69         s-1        PKC_DAG_Ca_PLCb3_Ca -\>
                                                      PKC_DAG_Ca+PLCb3_Ca_p

  k115f          0.12        0.12          s-1        PLCb4_Ca_p -\> PLCb4_Ca

  k117f          0.12        0.12          s-1        PLCb3_Ca_p -\> PLCb3_Ca

  k1f            177.47      177.47        μM-1 s-1   IP3R+IP3 -\> IP3R_IP3

  k1r            2.2         2.2           s-1        IP3R+IP3 \<- IP3R_IP3

  k2f            0.411       0.411         μM-1 s-1   IP3R_IP3+Ca -\> IP3R_IP3_Ca

  k2r            0.0434      0.0434        s-1        IP3R_IP3+Ca \<- IP3R_IP3_Ca

  k3f            0.9         0.9           μM-1 s-1   IP3R+Ca -\> IP3R_Ca

  k3r            0.806       0.806         s-1        IP3R+Ca \<- IP3R_Ca

  k4f            20          20            μM-1 s-1   IP3R_Ca+IP3 -\> IP3R_IP3_Ca

  k4r            0.029       0.029         s-1        IP3R_Ca+IP3 \<- IP3R_IP3_Ca
                                                      (thermcycle)

  k6f            10          10            μM-1 s-1   Ca+Buf -\> CaBuf

  k6r            7           7             s-1        Ca+Buf \<- CaBuf

  k33f           100         100           μM-1 s-1   PKC+DAG -\> PKC_DAG

  k33r           0.05        0.05          s-1        PKC+DAG \<- PKC_DAG

  k34f           10          10            μM-1 s-1   PKC_DAG+Ca -\> PKC_DAG_Ca

  k34r           6           6             s-1        PKC_DAG+Ca \<- PKC_DAG_Ca
                                                      (thermcycle)

  k35f           0.01        0.01          μM-1 s-1   PKC+Ca -\> PKC_Ca

  k35r           30          30            s-1        PKC+Ca \<- PKC_Ca

  k36f           1000        1000          μM-1 s-1   PKC_Ca+DAG -\> PKC_DAG_Ca

  k36r           0.0001      0.0001        s-1        PKC_Ca+DAG \<- PKC_DAG_Ca

  k37f           1           4.98          μM-1 s-1   GRKp+Gbg -\> GRKp_Gbg

  k37r           0.05        0.05          s-1        GRKp+Gbg \<- GRKp_Gbg

  k28af          158.49      77.52         μM-1 s-1   PKC_DAG_Ca+GRK -\> PKC_DAG_Ca_GRK

  k28ar          10          10            s-1        PKC_DAG_Ca+GRK \<- PKC_DAG_Ca_GRK

  k28bf          10          18.34         s-1        PKC_DAG_Ca_GRK -\> PKC_DAG_Ca+GRKp

  k49f           0.35        0.35          s-1        DAG -\> DAG_d

  Vqssk50        13.9        13.9          s-1        IP3+IP3K_a -\> IP4+IP3K_a (Vmax)

  Kqssk50        0.055       0.055         μM         IP3+IP3K_a -\> IP4+IP3K_a (Km)

  Vmaxk54        100         100           μM s-1     IP4 -\> IP5

  Kmk54          1.4         1.4           μM         IP4 -\> IP5

  k55f           0.008       0.008         s-1        IP5 -\> PIP2

  c2             0.185       0.185         none       ratio of ER volume/cell: de young

  v1             1E8         1E8           s-1        Ca channel flux constant

  v8             0.15        0.15          s-1        leak flux constant

  v4             20          20            μM s-1     maximum Ca uptake rate (SERCA)

  k4             0.65        0.65          μM         activation constant of SERCA pump

  a1             0.0055      0.0055        μM s-1     Ca leak into the cell from outside

  Kex            0.25        0.25          μM         Na/Ca exchange activation const

  Vex            0.023       0.023         μM s-1     maximum Ca exchange rate
  ----------------------------------------------------------------------------------------

Table S3: Parameter Posterior Uncertainty and References

This table shows the HPD intervals as computed by the R CODA library
function \"hpdinterval\". HPD intervals for each of the three MCMC
chains were calculated and the union of those intervals is reported for
each parameter in this table. The prior value reported in Table S2 was
set using information from references listed in the appropriate column.
The references used to form the basis of the parameter estimates are
shown in the last column. A detailed discussion of the choice of rate
constant estimates is shown in (3).

  ---------- -------------------------- ----------- ---------- ---------- ---------- -------------
                                        Parameter                                    
                                        HPD                                          
                                        Interval                                     

                                        mean        lower 95%  upper 95%  model      Reference

  k108f\*    UDP+p2yr -\> UDPC          12.85       6.64       18.47      13.20      

  k108r\*    UDP+p2yr \<- UDPC          3.54        1.88       5.01       3.62       

  k101f\*    c5a+c5aR -\> c5aC          134.61      32.34      197.77     92.41      

  k101r\*    c5a+c5aR \<- c5aC          0.67        0.04       1.00       0.38       

  k102af     GRKp_Gbg+c5aC -\>          591.54      591.54     591.54     591.54     
             GRKp_Gbg_c5aC                                                           

  k102ar     GRKp_Gbg+c5aC \<-          12.37       12.37      12.37      12.37      
             GRKp_Gbg_c5aC                                                           

  k102bf\*   GRKp_Gbg_c5aC \<-          378.66      118.54     660.84     199.31     
             GRKp_Gbg+c5aCp                                                          

  k104f      c5aCp -\> c5aR+c5a         1.00E-04    1.00E-04   1.00E-04   1.00E-04   

  k105f\*    c5aC+Gbg_Gai_GDP -\>       1.30E-02    1.09E-02   1.79E-02   1.29E-02   
             c5aC+Gbg+Gai_GTP                                                        

  k106f      Gai_GTP -\> Gai_GDP        0.02        0.02       0.02       0.02       

  k109f\*    UDPC+Gbg_Gaq_GDP -\>       1.36E-01    1.26E-01   1.51E-01   1.37E-01   
             UDPC+Gbg+Gaq_GTP                                                        

  k110f      Gaq_GTP -\> Gaq_GDP        0.02        0.02       0.02       0.02       

  k11f       Gai_GDP+Gbg -\>            7000.00     7000.00    7000.00    7000.00    
             Gbg_Gai_GDP                                                             

  k113f      Gaq_GDP+Gbg -\>            7000.00     7000.00    7000.00    7000.00    
             Gbg_Gaq_GDP                                                             

  k9af       RGS_a+Gai_GTP -\>          100.00      100.00     100.00     100.00     
             RGS_a_Gai_GTP                                                           

  k9ar       RGS_a+Gai_GTP \<-          0.10        0.10       0.10       0.10       
             RGS_a_Gai_GTP                                                           

  k9bf       RGS_a_Gai_GTP -\>          100.00      100.00     100.00     100.00     
             RGS_a+Gai_GDP                                                           

  k111af     RGS_a+Gaq_GTP -\>          100.00      100.00     100.00     100.00     
             RGS_a_Gaq_GTP                                                           

  k111ar     RGS_a+Gaq_GTP \<-          0.10        0.10       0.10       0.10       
             RGS_a_Gaq_GTP                                                           

  k111bf     RGS_a_Gaq_GTP -\>          100.00      100.00     100.00     100.00     
             RGS_a+Gaq_GDP                                                           

  k12f       PLCb4+Ca -\> PLCb4_Ca      20.00       20.00      20.00      20.00      (4, 5)

  k12r       PLCb4+Ca \<- PLCb4_Ca      8.00        8.00       8.00       8.00       (4, 5)

  k13f       PLCb4_Ca+Gaq_GTP -\>       62.55       62.55      62.55      62.55      (6, 7)
             PLCb4_Ca_Gaq_GTP                                                        

  k13r       PLCb4_Ca+Gaq_GTP \<-       10.63       10.63      10.63      10.63      (6, 7)
             PLCb4_Ca_Gaq_GTP                                                        

  k15af\*    PLCb4_Ca_Gaq_GTP+PIP2 -\>  1497.23     764.53     3041.57    1238.79    (6, 7)
             PLCb4_Ca+Gaq_GTP_PIP2                                                   

  k15ar      PLCb4_Ca_Gaq_GTP+PIP2 \<-  1.00        1.00       1.00       1.00       (6, 7)
             PLCb4_Ca+Gaq_GTP_PIP2                                                   

  k15bf\*    PLCb4_Ca+Gaq_GTP_PIP2 -\>  24.77       12.11      69.52      22.85      (6, 7)
             PLCb4_Ca+Gaq_GDP+IP3+DAG                                                

  k16f       PLCb3+Ca -\> PLCb3_Ca      20.00       20.00      20.00      20.00      (4, 5, 8, 9)

  k16r       PLCb3+Ca \<- PLCb3_Ca      8.00        8.00       8.00       8.00       (4, 5, 8, 9)

  k17f       PLCb3_Ca+Gaq_GTP -\>       50.00       50.00      50.00      50.00      (10, 11)
             PLCb3_Ca_Gaq_GTP                                                        

  k17r       PLCb3_Ca+Gaq_GTP \<-       0.10        0.10       0.10       0.10       (10, 11)
             PLCb3_Ca_Gaq_GTP                                                        

  k19af\*    PLCb3_Ca_Gaq_GTP+PIP2 -\>  176.85      30.58      302.61     70.88      \(10\)
             PLCb3_Ca_Gaq_GTP_PIP2                                                   

  k19ar      PLCb3_Ca_Gaq_GTP+PIP2 \<-  1.00        1.00       1.00       1.00       \(10\)
             PLCb3_Ca_Gaq_GTP_PIP2                                                   

  k19bf\*    PLCb3_Ca_Gaq_GTP_PIP2 -\>  32.19       12.24      56.67      27.90      \(10\)
             PLCb3_Ca+Gaq_GDP+IP3+DAG                                                

  k20f       Gbg+PLCb3_Ca -\>           8.35        8.35       8.35       8.35       (10, 12-15)
             PLCb3_Ca_Gbg                                                            

  k20r       Gbg+PLCb3_Ca \<-           0.39        0.39       0.39       0.39       (10, 12-15)
             PLCb3_Ca_Gbg                                                            

  k21af\*    PLCb3_Ca_Gbg+PIP2 -\>      162.54      149.74     179.55     165.83     (10, 12-15)
             PLCb3_Ca_Gbg_PIP2                                                       

  k21ar      PLCb3_Ca_Gbg+PIP2 \<-      8.00        8.00       8.00       8.00       (10, 12-15)
             PLCb3_Ca_Gbg_PIP2                                                       

  k21bf\*    PLCb3_Ca_Gbg_PIP2 -\>      5.49        5.09       5.90       5.42       (10, 12-15)
             PLCb3_Ca_Gbg+IP3+DAG                                                    

  k24af\*    PKC_DAG_Ca+PLCb4_Ca -\>    5.92        2.31       12.55      5.90       
             PKC_DAG_Ca_PLCb4_Ca                                                     

  k24ar      PKC_DAG_Ca+PLCb4_Ca \<-    11.00       11.00      11.00      11.00      
             PKC_DAG_Ca_PLCb4_Ca                                                     

  k24bf\*    PKC_DAG_Ca_PLCb4_Ca -\>    1.00        0.22       1.84       0.93       
             PKC_DAG_Ca+PLCb4_Ca_p                                                   

  k25af\*    PKC_DAG_Ca+PLCb3_Ca -\>    716.37      513.98     856.07     830.44     
             PKC_DAG_Ca_PLCb3_Ca                                                     

  k25ar      PKC_DAG_Ca+PLCb3_Ca \<-    11.00       11.00      11.00      11.00      
             PKC_DAG_Ca_PLCb3_Ca                                                     

  k25bf\*    PKC_DAG_Ca_PLCb3_Ca -\>    15.95       9.04       32.19      11.70      
             PKC_DAG_Ca+PLCb3_Ca_p                                                   

  k115f      PLCb4_Ca_p -\> PLCb4_Ca    0.12        0.12       0.12       0.12       

  k117f      PLCb3_Ca_p -\> PLCb3_Ca    0.12        0.12       0.12       0.12       

  k1f        IP3R+IP3 -\> IP3R_IP3      177.47      177.47     177.47     177.47     (16, 17)

  k1r        IP3R+IP3 \<- IP3R_IP3      2.20        2.20       2.20       2.20       (16, 17)

  k2f        IP3R_IP3+Ca -\>            0.41        0.41       0.41       0.41       (16, 17)
             IP3R_IP3_Ca                                                             

  k2r        IP3R_IP3+Ca \<-            0.04        0.04       0.04       0.04       (16, 17)
             IP3R_IP3_Ca                                                             

  k3f        IP3R+Ca -\> IP3R_Ca        0.90        0.90       0.90       0.90       (16, 17)

  k3r        IP3R+Ca \<- IP3R_Ca        0.81        0.81       0.81       0.81       (16, 17)

  k4f        IP3R_Ca+IP3 -\>            20.00       20.00      20.00      20.00      (16, 17)
             IP3R_IP3_Ca                                                             

  k4r        IP3R_Ca+IP3 \<-            0.03        0.03       0.03       0.03       (16, 17)
             IP3R_IP3_Ca (thermcycle)                                                

  k6f        Ca+Buf -\> CaBuf           10.00       10.00      10.00      10.00      

  k6r        Ca+Buf \<- CaBuf           7.00        7.00       7.00       7.00       

  k33f       PKC+DAG -\> PKC_DAG        100.00      100.00     100.00     100.00     (18, 19)

  k33r       PKC+DAG \<- PKC_DAG        0.05        0.05       0.05       0.05       (18, 19)

  k34f       PKC_DAG+Ca -\> PKC_DAG_Ca  10.00       10.00      10.00      10.00      (18, 19)

  k34r       PKC_DAG+Ca \<- PKC_DAG_Ca  6.00        6.00       6.00       6.00       (18, 19)
             (thermcycle)                                                            

  k35f       PKC+Ca -\> PKC_Ca          0.01        0.01       0.01       0.01       (18, 19)

  k35r       PKC+Ca \<- PKC_Ca          30.00       30.00      30.00      30.00      (18, 19)

  k36f       PKC_Ca+DAG -\> PKC_DAG_Ca  1000.00     1000.00    1000.00    1000.00    (18, 19)

  k36r       PKC_Ca+DAG \<- PKC_DAG_Ca  0.00        0.00       0.00       1.00E-04   (18, 19)

  k37f\*     GRKp+Gbg -\> GRKp_Gbg      4.76        3.97       6.94       4.98       (20, 21)

  k37r       GRKp+Gbg \<- GRKp_Gbg      0.05        0.05       0.05       0.05       (20, 21)

  k28af\*    PKC_DAG_Ca+GRK -\>         155.61      47.79      529.50     77.52      \(22\)
             PKC_DAG_Ca_GRK                                                          

  k28ar      PKC_DAG_Ca+GRK \<-         10.00       10.00      10.00      10.00      \(22\)
             PKC_DAG_Ca_GRK                                                          

  k28bf\*    PKC_DAG_Ca_GRK -\>         10.85       2.96       28.80      18.35      \(22\)
             PKC_DAG_Ca+GRKp                                                         

  k49f       DAG -\> DAG_d              0.35        0.35       0.35       0.35       

  Vqssk50    IP3+IP3K_a -\> IP4+IP3K_a  13.9        13.90      13.90      13.9       \(23\)
             (Vmax)                                                                  

  Kqssk50    IP3+IP3K_a -\> IP4+IP3K_a  0.0557      0.06       0.06       0.0557     \(23\)
             (Km)                                                                    

  Vmaxk54    IP4 -\> IP5                100         100.00     100.00     100        \(4\)

  Kmk54      IP4 -\> IP5                1.4         1.40       1.40       1.4        

  k55f       IP5 -\> PIP2               0.008       0.01       0.01       0.008      

  c2         ratio of ER volume/cell:   0.185       0.19       0.19       0.185      (16, 17)
             de young                                                                

  v1         Ca channel flux constant   1.00E+08    1.00E+08   1.00E+08   1.00E+08   (16, 17)

  v8         leak flux constant         0.15        0.15       0.15       0.15       

  v4         maximum Ca uptake rate     20          20.00      20.00      20         
             (SERCA)                                                                 

  k4         activation constant of     0.65        0.65       0.65       0.65       
             SERCA pump                                                              

  a1         Ca leak into the cell from 0.0055      0.01       0.01       0.0055     
             outside                                                                 

  Kex        Na/Ca exchange activation  0.25        0.25       0.25       0.25       
             const                                                                   

  Vex        maximum Ca exchange rate   0.023       0.02       0.02       0.023      
  ---------- -------------------------- ----------- ---------- ---------- ---------- -------------

Table S4: Goodness of Fit Evaluation

We use the mean squared error criterion to evaluate the goodness of our
model fit to the data. We have used this data in the estimation
procedure and thus does not constitute a true validation. However, we
show that in general our model fits the bulk of the data. Those areas of
lack-of-fit are usually due to extraordinary experiment-to-experiment
variation and in some cases point to unaccounted mechanisms. We
elaborate on one such mechanism (multiple GRK isoforms) in the text of
the article.

![](media/image36.png)

Protocol 1: FITC Protocol

1.  FITC soln at 400nM used for robotic addition to wells.  A 4-fold
    in-well\
    dilution yielded 100nM final in a final 100ul well volume.

2.  Wells contained 75 ul water.

3.  Instrument settings:\
            Flex mode = serial reads at FITC wavelengths (495ex/ 525em,
    510\
    cutoff)\
            Robotic additions at 20 seconds\
            Additions defined by time / volume / ejection height /
    ejection\
    speed plus\
                    trituration \# cycles / volume / height (speed is
    defined\
    by above)

4.  Settings for first vs second data set were:\
            25ul volume / 75ul height / speed 1\
            25ul volume / 50ul height / speed 4 plus 1 trituration @
    25ul\
    volume, 50ul height

# References