The overall aim of this procedure is to estimate the relative affinity constant KB of an agonist for the active state of a receptor by analysis of its concentration response curve. This is accomplished by first measuring the concentration response curves of a group of agonists for eliciting a response at a G-protein coupled receptor. The next step of the procedure is to estimate the eemax and EC 50 values of the agonists using non-linear regression analysis.
These values are then used to calculate initial parameter estimates for the subsequent non-linear regression analysis involving the operational model. As a final step, relative estimates of the affinity constants of agonists for the active state of the receptor are obtained using global nonlinear regression analysis of their concentration response curves. Ultimately using a modified form of the operational model, the affinity constant of an agonist for the active state of a receptor expressed relative to that of another agonist can be estimated through global nonlinear regression analysis of their concentration response curves.
This method can help answer key questions in the drug discovery field, such as does an agonist have selectivity for a specific signaling pathway? Generally, individuals new to this method will struggle because of the details of the mathematical analysis. For estimation of relative agonist KB values, a series of at least two agonist concentration response curves is required.
A discussion of considerations for such experiments can be found in the written protocol. After obtaining the response curves, subtract the basal response from that measured in the presence of each concentration of agonist begin to enter the data from the concentration response experiments into a data table. In the Prism software, all of the log agonist concentrations are entered under the column labeled X.The response measurements for the agonist that appears to have the largest maximal response or eax value are entered into column A and those for other agonists are entered into adjacent lettered columns.
Enter replicate measurements of concentration response curves into sub columns of a given lettered column. Select the graph sheet on which the data are plotted and select analyze to analyze the data by non-linear regression analysis using the variable slope equation, constrain the parameter bottom to zero and perform the regression analysis. Record the parameters top and log EC 50 for use in the calculation of initial parameter estimates.
To calculate the initial parameter estimates, assign log tau K observed to the negative log EC 50 value of the standard agonist. Next, calculate the log RAI value of each test agonist as the logarithm of the quantity consisting of the product of the eemax value of the test agonist times the EC 50 of the standard agonist divided by the product of the emax value of the standard agonist times the EEC 50 of the test agonist. In this equation, the parameters of the standard agonist are denoted with an apostrophe.
Then assign the log affinity Constance of the test agonist to the negative log of their respective EC values. After entering the data into Prism, ensure that the data for the agonist with the largest EMAX value are entered into column A.This agonist is now designated as the standard, whereas the other agonists are designated as test agonists. Next, enter a user-defined equation log, RAI into prism on several lines.
In this case, the user-defined equation involves a total of five agonists. Enter the initial parameter estimates of lock R and the affinity Constance of the test agonists. M sis is assigned the EMAX value of the standard agonist and M is assigned a value of one.
Now enter the initial parameter estimates of the log RAI values of the test agonists. Apply parameter constraints by constraining log K one to zero, and by setting log GR, m, sis, and M to a shared value for all data sets. Next, initiate non-linear regression analysis.
The results yield the log K observed and log RAI values of the test agonists for estimation of agonist KB values in absolute units of inverse molar units, cell-based vitro assays are used that exhibit constitutive receptor activity. Choose agonists and design the experiment as described in the written protocol. Calculate constitutive receptor activity and the response to each concentration of agonist as the measured response minus the basal response in cells, not transfected with the receptor shown here a responses to various agonists calculated in this manner for a signaling pathway, exhibiting very low constitutive activity for preliminary analysis.
First, enter the data into prism as described for non constitutive activity.Accept. Also enter the response caused by constitutive receptor activity in the appropriate lettered columns in the row corresponding to a log agonist concentration of negative 20. Here a large negative logarithm is entered to approximate an agonist concentration of zero.
Analyze the data as before, except that for constitutive activity, the parameter bottom should be constrained so that it is shared for all data sets. Record the shared parameter as well as the parameters top and log EC for each agonist. After determining the log affinity Constance of the standard agonist in separate experiments, calculate the initial estimate of the log K observed value of each partial test agonist as the logarithm of the expression consisting of the difference between the emax value of the standard agonist and the test agonist divided by the product of the EC 50 and the difference between the eemax value of the standard agonist and the constitutive response.
Calculate the initial estimate of log KB for each agonist and the initial estimate of log T cis to estimate agonist KB values. Enter the data into Prism and then enter a user-defined equation. Log KB into prism on several lines as demonstrated here for the condition of two agonists.
Next, enter the initial parameter estimates by inputting the affinity stance of each agonist. The log T sis estimate the M sis estimate and the M estimate M sis is assigned the EMAX value of the standard agonist and M is assigned a value of one. Finally, enter the initial estimates of log kb.
Apply parameter constraints by constraining log K one to its previously determined value, and by setting log T sis, m sis, and M to a shared value for all data sets. Initiate non-linear regression analysis. The results yield the log KB of the standard agonist, the log K observed, and the log KB values of partial agonists.
The maximal response of the system, the log T cys value for the free receptor complex, and the transducer slope factor in the operational model shown here is muscarinic agonist induced phosphoinositide hydrolysis in Chinese hamster ovary cells, stably expressing the M three muscarinic receptor. The concentration response curves of selected muscarinic agonists were measured in this assay, and the data were analyzed as described here to estimate the KB value of each agonist expressed relative to that of Oxo Tremaine M.The theoretical curves represent the least squares fit of the regression equation to the data. The log RAI estimates are shown for kabale, a recline, pilocarpine, and McNeil.
A 3, 4 3. The corresponding estimates of the maximum response of the system and the transducer slope factor were determined. The log K observed values of the agonists were also found for each agonist shown.
Here are the results of experiments on muscarinic agonist stimulated phosphoinositide hydrolysis in HC 2 93 cells. Stably expressing G alpha 15 transient expression of the M three muscarinic receptor caused an increase in basal phosphoinositide hydrolysis, which was attributed to constitutive receptor activity. The data were analyzed to estimate the log KB values of Oxo Tremaine M and MacNeil, A 3 43.
The theoretical curves represent the least squares fit of the regression equation to the data. The log KB estimates are shown for Oxo Tremoring M and McNeil, A 3 43. The estimate of the K observed value of McNeil A 3 43 was also determined.
Once mastered, this data analysis technique can be done in a few minutes if done properly. After watching this video, you should have a good understanding of how to estimate both relative and actual KB values from the concentration response curves of agonists for eliciting a response downstream in the signaling pathway of a G protein coupled receptor.
