The protocol and algorithm were developed within a project financed by the Deutsche Forschungsgemeinschaft (DFG grant SFB1009 A09 and EB177/13-1). The author thanks Barbara Schedding and Felix Schmalbein for technical support and Dr. Niland for critically reading the manuscript.

1. Stock Solutions
<ol>
	<li>To prepare 100 mL of 10x&#160;TBS pH 7.4 solution, dissolve 6.06 g of TRIS and 8.77 g of NaCl in 90 mL of deionized water, adjust the pH to 7.4 with 37% HCl solution, fill the volume to 100 mL with deionized water, and filter the solution.</li>
	<li>To prepare 100 mL of 1 M HEPES/NaOH, pH 7.4 solution, dissolve 23.83 g of HEPES in 90 mL of deionized water, adjust the pH to 7.4 with 1.5 M NaOH, fill the volume to 100 mL with deionized water, and filter the solution.</li>
	<li>To prepare 100 mL of 5 M NaCl solution, dissolve 29.2 g of NaCl in 90 mL of deionized water. Fill the volume to 100 mL with deionized water and filter the solution.</li>
	<li>To prepare 100 mL of 1 M MgCl2 solution, dissolve 20.33 g of MgCl2 &#183; 6H2O in 90 mL of deionized water. Fill the volume to 100 mL with deionized water and filter the solution.</li>
	<li>To prepare 5% heat-inactivated BSA in water, weigh 2.5 g of BSA (fraction V, pH 7.0) in a 50 mL tube and dissolve it in 45 mL of deionized water. Fill the solution to 50 mL with deionized water, and heat the solution in a water bath at 68 &#176;C for 45 min. Cool it in an ice bath and store it at -20 &#176;C.</li>
	<li>Prepare aqueous 25% glutaraldehyde solution. 
	CAUTION: Glutaraldehyde is harmful if swallowed, toxic by inhalation, and causes burns. Wear protective clothing, gloves, and eye/face protection.</li>
	<li>Raise the rabbit antiserum as previously described19. The titer of antiserum was determined according to standard protocols20.</li>
	<li>Prepare anti-rabbit immunoglobulin-antibodies from goat conjugated with alkaline phosphatase.</li>
	<li>To prepare 100 mL of 0.1 M glycine solution, dissolve 0.75 g of glycine in 90 mL of deionized water. Adjust the pH to 10.4 with 1.5 M NaOH solution, fill the volume to 100 mL with deionized water, and filter the solution.</li>
	<li>To prepare 100 mL of 0.5 M Zn(II)-acetate solution, dissolve 10.98 g of Zn(II)-acetate &#183; 2H2O in 90 mL of deionized water. Fill the volume to 100 mL with deionized water and filter the solution.</li>
	<li>To prepare 100 mL of 1.5 M NaOH solution, dissolve 6.0 g of NaOH in 90 mL of deionized water. Fill the volume to 100 mL with deionized water and filter the solution.</li>
</ol>
2. Prepare Buffers and Working Solutions
<ol>
	<li>Dilute 5 mL of 10x&#160;TBS pH 7.4, with 45 mL deionized water and add 100 &#181;L of a 1 M MgCl2 stock solution. Keep it at room temperature. The TBS, pH 7.4, 2 mM MgCl2 solution is for immobilization of the receptor and washing the microtiter plate.</li>
	<li>Dilute 10 mL of 5% of heat-inactivated BSA in water and 5 mL of 10x&#160;TBS, pH 7.4 with deionized water to 50 mL. Add 100 &#181;L of 1 M MgCl2 stock solution and mix the solution well. Keep it on ice and store it for further experiments at -20 &#176;C. Note that 2.5 mL of 1% BSA in TBS, pH 7.4, 2 mM MgCl2 are required for each titration curve.</li>
	<li>Dilute 2.5 mL of 1 M HEPES/NaOH, pH 7.4 and 1.5 mL 5 M NaCl solution to 50 mL with deionized water, add 100 &#181;L 1 M MgCl2 solution, and mix the solution thoroughly to prepare 50 mL of HBS, pH 7.4: 50 mM HEPES/NaOH, 150 mM NaCl.</li>
	<li>Add 5 &#181;L of 1M MgCl2 stock solution and 2 &#181;L 0.5 M Zn(II)-acetate stock solution to 5 mL 0.1 M glycine solution, pH 10.4 to prepare alkaline phosphatase (AP) buffer (0.1 M glycine solution, pH 10.4, 1 mM MgCl2, 0.2 mM Zn(II)-acetate).</li>
</ol>
3. Immobilization of the Receptor (Integrin &#945;2A-Domain) to a Microtiter Plate
<ol>
	<li>Dilute the stock solution of integrin &#945;2A-domain in TBS, pH 7.4, 2 mM MgCl2 for a final concentration of 5 &#181;g/mL. 
	NOTE: The volume of the coating solution is 650 &#181;L for one titration curve comprising a 12 well-row of a half area-microtiter plate.</li>
	<li>Fill every well of a row on a half area-microtiter plate with 50 &#181;L/well of the 5 &#181;g/mL coating solution of integrin &#945;2A-domain (wild-type or mutant). Perform every titration row at least in duplicates (in this example as quadruplets; see layout of microtiter plate in Figure 1).</li>
	<li>Seal the plate with foil or close it with a lid. Leave the plate at 4 &#176;C overnight.</li>
</ol>
4. Wash Coated Wells of the Plate Twice with TBS, pH 7.4, 2 mM MgCl2
<ol>
	<li>To remove soluble receptor molecules, which have not been immobilized to the plastic surface by physical adsorption, remove the coating solution and fill each well with 50 &#181;L of TBS, pH 7.4, 2 mM MgCl2.</li>
	<li>Remove the wash solution. Ensure that the wells do not become dry. Therefore, do not tap the microtiter plate onto a tissue cloth to remove residual fluid. Use a multistep pipette or a multi-channel pipette to fill the wells quickly.</li>
	<li>Repeat this washing step once.</li>
</ol>
5. Block Nonspecific Binding Sites
<ol>
	<li>Add 50 &#181;L of 1% BSA solution in TBS, pH 7.4, 2 mM MgCl2 to each well.</li>
	<li>Reseal the wells with foil or close with a lid.</li>
	<li>Incubate the wells for 1 h at room temperature. 
	NOTE: Any of the incubation steps of this protocol can be performed on a rocking or shaking platform. However, this is not required and does not alter the outcome of the experiment.</li>
</ol>
6. Preparation of a Serial Dilution Row of the Ligand, Rhodocetin
<ol>
	<li>Vary the start concentration of rhodocetin and the dilution factor of the serial dilution, to obtain an appropriate range of ligand concentrations and to record a full titration curve with a minimum and maximum signal. In this experiment, employ a start concentration of 243 nM rhodocetin and a dilution factor of 2.3. Dilute the rhodocetin stock solution to the highest ligand concentration of the serial dilution row. For each titration curve with a dilution factor of 2.3, prepare 115 &#181;L of 243 nM (i.e., 15,2 &#181;g/mL) rhodocetin solution in 1% BSA/TBS, pH 7.4, 2 mM MgCl2 in test tube #1.</li>
	<li>Fill 65 &#181;L of 1% BSA solution in TBS, pH 7.4, 2 mM MgCl2 in 10 test tubes, labeled #2 through #11.</li>
	<li>Transfer 50 &#181;L of the rhodocetin dilution from test tube #1 to test tube #2, mix both solutions (total volume: 115 &#181;L; dilution factor: 1:2.3) by trituration, and then transfer 50 &#181;L from this mixture to test tube #3, etc.</li>
	<li>Continue this serial dilution until test tube #11. 
	NOTE: The volumes given in steps 6.1 - 6.4 are sufficient for one titration curve. Multiply these volumes by the number of replicates. In this case, perform eight titration curves (quadruplets of two &#945;2A-domain forms) and prepare the following volumes: 920 &#181;L of rhodocetin solution at the highest concentration in test tube #1; 520 &#181;L of 1% BSA in TBS, pH 7.4, 2 mM MgCl2 to fill in each of the test tubes #2 to #11; and 400 &#181;L of transfer volume from one tube to the next one.</li>
</ol>
7. Binding of Ligand (Rhodocetin) at Different Concentrations to Immobilized Receptor (Integrin &#945;2A-Domain)
<ol>
	<li>Remove the blocking solution from the microtiter plate wells by a vacuum line.</li>
	<li>Immediately add 50 &#181;L of the rhodocetin solution in 1% BSA/TBS, pH 7.4/MgCl2 solution of test tube #1 into wells of column 1, solution of test tube #2 to wells of column 2,etc. Add 50 &#181;L of 1% BSA in TBS, pH 7.4, 2 mM MgCl2 (blocking and dilution buffer) as a ligand-free control to wells of column 12 (see layout of microtiter plate, Figure 1).</li>
	<li>Reseal the wells with foil or close with a lid.</li>
	<li>Incubate the wells for 1.5 h at room temperature (around 20 - 22 &#176;C).</li>
</ol>
8. Wash Wells of Plate Twice with HBS, pH 7.4, 2 mM MgCl2
<ol>
	<li>To remove non-bound ligand molecules, remove the binding solution and fill each well with 50 &#181;L of HBS, pH 7.4, 2 mM MgCl2. Then, remove the wash solution.</li>
	<li>Take care that the wells do not become dry. Therefore, do not tap the microtiter plate onto a tissue cloth to remove residual fluid. Use a multistep pipette or a multi-channel pipette to fill the wells quickly.</li>
	<li>Repeat this washing step once.</li>
</ol>
9. Fix the Receptor-bound Ligand with 2.5% Glutaraldehyde in HBS, pH 7.4, 2 mM MgCl2
<ol>
	<li>Prepare a fresh 2.5% glutaraldehyde solution by mixing 1 part of 25% glutaraldehyde solution and 9 parts of HBS, pH 7.4, 2 mM MgCl2.</li>
	<li>Fill every well of the microtiter plate with 50 &#181;L of the 2.5% glutaraldehyde solution in HBS, pH 7.4, 2 mM MgCl2. Incubate the microtiter plate for 10 min at room temperature.</li>
</ol>
10. Wash Wells of the Plate Three Times with 50 &#181;L/well of TBS, pH 7.4, 2 mM MgCl2
<ol>
	<li>To remove and inactivate excess glutaraldehyde, remove the fixation solution and fill each well with 50 &#181;L of TBS, pH 7.4, 2 mM MgCl2. Then remove the wash solution. 
	NOTE: Pour the glutaraldehyde-containing fixation solution from the microtiter plate into a dish and discard the fixation solution after it has been inactivated by an equal volume of TBS, pH 7.4.</li>
	<li>Take care that the wells do not become dry. Therefore, do not tap the microtiter plate onto a tissue cloth to remove residual fluid. Use a multistep pipette or a multi-channel pipette to fill the wells quickly.</li>
	<li>Repeat this washing step twice.</li>
</ol>
11. Quantification of Receptor-bound Ligand by ELISA
<ol>
	<li>Add 50 &#181;L/well of the primary antibody solution in 1% BSA in TBS, pH 7.4, 2 mM MgCl2. The primary antibody solution is a rabbit antiserum raised against rhodocetin19, diluted 1:2,000 in 1% BSA in TBS, pH 7.4, 2 mM MgCl2.</li>
	<li>Incubate the plate for 75 - 90 min at room temperature. Wash all wells of the plate three times with 50 &#181;L/well of TBS, pH 7.4, 2 mM MgCl2. During the three washing steps, tapping of the microtiter plate onto a tissue cloth is not required.</li>
	<li>Add 50 &#181;L/well of the secondary antibody solution in 1% BSA in TBS, pH 7.4, 2 mM MgCl2. To this end, dilute the secondary antibody, rabbit immunoglobulin-targeting goat antibodies conjugated with alkaline phosphatase, to 1:2,000 in 1% BSA in TBS, pH 7.4, 2 mM MgCl2. Incubate the plate for 75 - 90 min at room temperature.</li>
	<li>Prepare AP-detecting solution by dissolving a 5 mg tablet containing 4-nitrophenyl phosphate disodium salt hexahydrate (phosphatase substrate) in 5 mL of AP buffer (0.1 M glycine solution, pH 10.4, containing 1 mM MgCl2 and 0.2 mM Zn(II)-acetate).</li>
	<li>Wash all wells of plate three times with 50 &#181;L/well of TBS, pH 7.4, 2 mM MgCl2, immediately before performing the next step. Tap the microtiter plate onto a tissue cloth after the last washing step to remove all traces of liquid.</li>
	<li>Add 50 &#181;L/well of the AP-detecting solution to the wells of the microtiter plate. Add AP-detecting solution promptly to all wells to start the enzymatic conversion as simultaneously as possible. Therefore, use a multi-channel pipette.</li>
	<li>Incubate the plate at room temperature until the solution in the wells with the highest ligand concentration turn yellow. 
	NOTE: The incubation time may vary between 5 min and 1 h depending on the signal intensity.</li>
	<li>Stop conversion of the phosphatase substrate by adding 50 &#181;L/well of 1.5 M NaOH solution. Leave the plate standing for several minutes to ensure streak-free mixing of both solutions. To warrant the same incubation period in all wells, use a multi-channel pipette and add the 1.5 M NaOH in the same order added to the wells as that of the AP-detecting substrate in step 11.8.</li>
	<li>Measure the optical density (OD) at 405 nm of each well by an ELISA reader.</li>
</ol>
12. Evaluation of the Titration Signals
<ol>
	<li>Open the table of raw data, the OD405nm values, with Excel. As these signal values of the titration curves are read in rows, transpose the values to a column and label with the concentrations of added ligand in another column.</li>
	<li>Open the Graphpad Prism 5 (Version 5.0). Open a new project file in the main menu. Choose the XY format under New data &#38; graph. Choose the option Enter and plot a single point for each value for the Y-axis.</li>
	<li>Copy the two columns, concentration of added ligand and signal values (OD405nm values) from the excel file and paste them into the data sheet of GraphPad Prism as X and Y values, respectively.</li>
	<li>Open the Analysis sub-program of GraphPad Prism 5 and choose the option Non-linear regression under XY-analysis. Choose user-defined equation and press the New button to create a new equation.</li>
	<li>Type the titration curve equation in the form: Y =(Smax-Smin)*((X+R+K)-sqrt((X+R+K)^2-4*R*X))/(2*R)+Smin + B*X into the newly opened template sheet, with Y being the signal value S, X being the concentration of added ligand L, R being the concentration of immobilized receptor, K being the dissociation constant, and B being the background slope. Define the appropriate constraints, such as K &#62;0 and R &#62;0. 
	NOTE: This equation is the same equation of equation 9 in a different form.</li>
	<li>Analyze the values of the data sheet by choosing the user-defined equation, which was newly created. Open the table with the calculated approximation values (K, Rt, Smax, Smin, and B) which are shown under the Result section on the left side of the software screen. 
	NOTE: The software determines the 5 parameters by iterative fitting of the non-linear regression only if the titration curve consists of at least 5 data points.</li>
	<li>Evaluate the parameters K, Rt, Smax, Smin, and B for every group of titration curves statistically, and correlate the parameters with the specific feature of the group (mutated or chemically-modified ligand or receptor).</li>
</ol>

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The author has nothing to disclose.

The titration ELISA is a versatile test system to determine the dissociation of a receptor-ligand interaction. As the titration ELISA circumvents the necessity to separate free and bound ligands effectively and to analyze their concentrations quantitatively, substantially more studies and publications have employed titration ELISAs instead of recording binding curves. Moreover, titration ELISAs are easy to perform and require reasonably low amounts of receptor and ligand. For accurate analysis of dissociation constants, ...

The dissociation constant K is a key parameter to describe the affinity of a receptor (R) for its ligand (L). Based on the law of mass action, K is defined for the equilibrium, in which the receptor-ligand complex RL dissociates into the receptor R and the ligand L:
<img alt="Equation 1 " src="/files/ftp_upload/57334/57334eq1.jpg" />&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;Equation 1
with the indices f indicating the free/unbound state of receptor and ligand. The concentration of the receptor-ligand complex, RL, is identical to the concentration of the receptor-bound ligand Lb. As the total concentration of receptor Rt is the sum of the free receptor Rf and ligand-bound receptor Rb = Lb, the dissociation constant can also be written as:
<img alt="Equation 2 " src="/files/ftp_upload/57334/57334eq2.jpg" />&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;Equation 2
Therefore, the saturation yield Y, defined as the fraction of bound ligand Lb in relation of the total concentration of receptor Rt,
<img alt="Equation 3 " src="/files/ftp_upload/57334/57334eq3.jpg" />&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;Equation 3
depends on the concentration of free ligand Lf:
<img alt="Equation 4 " src="/files/ftp_upload/57334/57334eq4.jpg" />&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;Equation 4
This hyperbolic relation describes the binding curve of a receptor-ligand interaction and its plot shows the concentration of bound ligand Lb as a function of the concentration of free ligand Lf. From the binding curve, the dissociation constant K can be derived as the concentration of free ligand at half-maximal saturation yield. Moreover, different algorithms to linearize binding curves have been established, such as the double-reciprocal plot by Klotz1,2, or transformations according to Scatchard or Hanes (reviewed by Bisswanger3). However, all algorithms suffer from the problem that the maximum value of the saturation yield, which is asymptotically approached at high concentrations of free ligand in the binding curve, has to be estimated in a graphical pre-evaluation and therefore is error-prone.
In addition, the determination of a binding curve requires the quantification of free and bound ligand during the binding equilibrium. To this end, the free ligand has to be separated from the receptor-bound ligand and quantified. Therefore, the ligand and receptor have to differ in their properties, such as a non-protein ligand as opposed to a protein receptor. If both binding partners are proteins, they have to be distinguishable in their sizes, charges, or other molecular features. Nevertheless, the quantification of ligand concentrations in small-scale binding approaches is a difficult task. Radioactive labeling of the ligand has often been necessary to detect the low concentration of bound ligand, especially if substantial amounts of receptors were not available or affordable. Moreover, the receptor-bound ligand may dissociate during and after isolation in a non-negligible manner. Hence, complex methods, such as equilibrium gel filtration4, capillary electrophoresis5, and pulse proteolysis6, are required to quantify receptor-bound ligand and separate it from free ligand.
In contrast to these binding assays, titration experiments do not require the quantitative separation of bound and free ligand. To this end, a receptor at a constant concentration is titrated with different concentrations of added ligand. By binding to the receptor, the bound ligand has a biophysical property which distinguishes it from the free ligand and is measurable by, e.g., photometry, fluorometry, or antibody detection. Thus, a signal S, which is proportional to the saturation yield Y and consequently also to the concentration of receptor-bound ligand (Lb), is detected as a function of the total concentration of added ligand (Lt). Both parameters, the signal S and the total concentration of added ligand are quantified in a direct and easier manner than the concentrations of bound and free ligand. Especially, the detection of receptor-bound ligand by enzyme-linked immunosorbent assay (ELISA) allowed the reduction of sample volumes to below 100 &#181;L as well as parallel measurements of several ligand concentrations in multi-well microtiter plates. In a titration ELISA, a receptor is physically adsorbed to a microtiter plate at the same concentration and titrated with soluble ligand. The receptor is immobilized to the plastic surface essentially by hydrophobic adsorption. The surface concentration of immobilized receptor correlates with the coating concentration of the receptor in a nonlinear relation, likely according to Langmuir&#180;s adsorption isotherm7. In addition to the overall number of adsorbed receptor molecules, their activity state is another important parameter for titration assays. Only immobilized receptors which have retained ligand binding activity, are relevant for the titration assay and eventually contribute to the total concentration of active receptors Rt of the titration assay, which cannot be determined directly.
Sites on the plastic surface, which are not covered by the immobilized receptor are prone to adsorb other proteins, such as the ligand. Physical adsorption of the ligand to such plastic surface sites would result in a similar signal as the receptor-bound ligand, yet in a nonspecific manner. To reduce this nonspecific signal, the plastic surface sites of the microtiter plates which have not been coated with protein yet will be blocked with bovine serum albumin (BSA). However, for some receptor-ligand titration assays, nonspecific background signals may be observed. Then, other blocking agents, such as a solution of 0.2% gelatin or of 0.04% Tween 20, are recommended.
After binding to the receptor, the free ligand is removed by two washing steps. Bound ligand remains with the receptor, which is immobilized to the plastic surface of the microtiter well, and optionally reinforced by chemical fixation. For the subsequent covalent cross-linkage of bound ligand and immobilized receptor with glutaraldehyde, the buffer substance TRIS is replaced for HEPES, without any change in ligand binding. HEPES, in contrast to TRIS, does not inactivate glutaraldehyde. The covalent cross-linkage with glutaraldehyde fixes the bound ligand with its receptor and prevents its dissociation during subsequent washing and incubation steps. Thus, the receptor-ligand interaction is chemically frozen and warrants a titration curve which is unaffected by subsequent steps of washing and incubation. However, glutaraldehyde fixation may chemically modify the ligand and receptor in such a way that their interaction is reduced or abolished. Moreover, modification of epitopes within the ligand may change the binding affinity of the detecting antibody, especially if a monoclonal antibody is used to quantify bound ligand. Although neither of these adverse effects of glutaraldehyde fixation occurs in this titration ELISA, the sensitivity of the test towards glutaraldehyde must be tested for every receptor-ligand interaction prior to the titration experiment. After fixation, excess glutaraldehyde is removed in three washing steps with TRIS-containing buffer. TRIS inactivates remaining aldehyde groups, which might nonspecifically react with detecting antibodies in the subsequent step.
The amount of bound ligand is quantified with enzyme-linked antibodies, which provide a photometric ELISA signal S. This is plotted versus the total ligand concentration Lt added to each well. Despite its easier acquisition, the titration curve is not a hyperbolic function in contrast to the binding curve. Furthermore, it has been unclear how to calculate the dissociation constant K from a titration curve. Although algorithms to linearize spectroscopically acquired titration curves have been independently reported by Stockell8 and Heyn and Weischet9, they fell short due to their uncertainty of estimating the maximum signal value that the saturation yield approaches at high concentrations of added ligand.
Here, a titration ELISA and a non-linear regression algorithm are described to derive the dissociation constant K for a receptor ligand interaction from a titration curve. This protocol is exemplified for the interaction of the collagen-binding A-domain of the integrin &#945;2&#946;1 with a snake venom-derived inhibitor. Integrins are cell adhesion molecules, which mediate the anchorage of cells to the surrounding extracellular matrix or the underlying basement membrane10,11. Moreover, integrins convey important signals between cells and the extracellular matrix by recruiting additional signaling molecules and forming new cell organelles, adhesomes, upon cell-matrix interaction12,13,14. Collagen, the ligand of &#945;2&#946;1 integrin, is the most abundant protein of the human body and is a crucial scaffolding component of the connective tissue15. The interaction between &#945;2&#946;1 integrin and collagen is mediated by the A-domain of the integrin &#945;2 subunit. The integrin &#945;2A-domain contains a divalent cation, which is required for collagen binding and stabilizes its structure. The wild-type form as well as mutants of the &#945;2A domain, such as the one in which the surface-exposed residue Y216 had been replaced for a glycine, can easily be produced recombinantly in a bacterial expression system and isolated via their oligo-His-tags with a NiNTA superflow column with a subsequent dialysis against TRIS-buffered saline (TBS; 50 mM TRIS/HCl, pH 7.4, 150 mM NaCl) containing 2 mM MgCl216. Their concentrations were determined with the bicinchoninic acid assay (BCA) and their purities are tested by conventional SDS-PAGE and stained with Coomassie-Brilliant Blue R250.
The interaction between &#945;2&#946;1 integrin and collagen is blocked by binding of the snake venom component, rhodocetin, from the Malayan pit viper (Calloselasma rhodostoma)16,17. Used as a soluble ligand in this titration ELISA, rhodocetin was purified from the crude venom as described previously16. It is dissolved in HEPES-buffered saline (HBS; 10 mM HEPES/NaOH, pH 7.4, 150 mM NaCl) and is stored frozen at -20 &#176;C. Its concentration was determined by BCA and its purity was proven by SDS-PAGE. As an antagonist, rhodocetin not only blocks collagen binding to the integrin &#945;2&#946;1 A-domain, but also stabilizes the inactive conformation of the integrin thereby preventing any signaling from collagen into cells or platelets18. It is of great biomedical importance to determine the dissociation constant of rhodocetin with its receptor target and thus unravel its molecular mechanism and pharmaceutical potential e.g., as an antithrombotic agent. To this end, a titration ELISA is described including its evaluation, which is applicable to almost any receptor-ligand interaction with a 1:1 interaction stoichiometry.

<table><tbody><tr><td>TRIS</td><td>neoFrox</td><td>1125KG001</td><td></td></tr><tr><td>HEPES</td><td>Sigma-Aldrich</td><td>H4034</td><td></td></tr><tr><td>NaCl</td><td>Applichem</td><td>1,316,591,214</td><td></td></tr><tr><td>MgCl&lt;sub&gt;2&lt;/sub&gt;</td><td>Merck</td><td>172571</td><td></td></tr><tr><td>integrin a2A, wild-type and mutant, recombinant</td><td></td><td>isolated in author&#039;s lab</td><td></td></tr><tr><td>NiNTA superflow column&amp;nbsp;</td><td>Qiagen, Germany</td><td>30821</td><td></td></tr><tr><td>Coomassie-Brilliant Blue R250</td><td>Serva</td><td>35050</td><td></td></tr><tr><td>bicinchoninic acid assay (BCA), protein concentration determination kit</td><td>Fisher Scientific</td><td>23225</td><td></td></tr><tr><td>bovine serum albumine (BSA), fraction V</td><td>Applichem</td><td>A1391</td><td></td></tr><tr><td>25 % solution of glutaraldehyde</td><td>Merck</td><td>354400</td><td></td></tr><tr><td>anti-rabbit immunglobulin-antibodies from goat, conjugated with alkaline phosphatase</td><td>Sigma-Aldrich</td><td>A9919</td><td></td></tr><tr><td>Glycine</td><td>Applichem</td><td>A1377</td><td></td></tr><tr><td>Zn(II)-acetate</td><td>Applichem</td><td>A4324</td><td></td></tr><tr><td>NaOH</td><td>Applichem</td><td>A1551</td><td></td></tr><tr><td>Alkaline phosphatase substrate tablet (5 mg)</td><td>Sigma-Aldrich</td><td>S0942</td><td></td></tr><tr><td>Costar half-area microtiter plate</td><td>Thermo Scientific</td><td>Corning 3690</td><td></td></tr><tr><td>micro reaction tubes</td><td>Eppendorf</td><td>30120086</td><td></td></tr><tr><td>Microplate ELISA reader</td><td>BioTek</td><td>Synergy HT</td><td></td></tr></tbody></table>

titration elisa as a method to determine the dissociation constant of receptor ligand interaction

The dissociation constant describes the interaction between two partners in the binding equilibrium and is a measure of their affinity. It is a crucial parameter to compare different ligands, e.g., competitive inhibitors, protein isoforms and mutants, for their binding strength to a binding partner. Dissociation constants are determined by plotting concentrations of bound versus free ligand as binding curves. In contrast, titration curves, in which a signal that is proportional to the concentration of bound ligand is plotted against the total concentration of added ligand, are much easier to record. The signal can be detected spectroscopically and by enzyme-linked immunosorbent assay (ELISA). This is exemplified in a protocol for a titration ELISA that measures the binding of the snake venom-derived rhodocetin to its immobilized target domain of &#945;2&#946;1 integrin. Titration ELISAs are versatile and widely used. Any pair of interacting proteins can be used as immobilized receptor and soluble ligand, provided that both proteins are pure, and their concentrations are known. The difficulty so far has been to determine the dissociation constant from a titration curve. In this study, a mathematical function underlying titration curves is introduced. Without any error-prone graphical estimation of a saturation yield, this algorithm allows processing of the raw data (signal intensities at different concentrations of added ligand) directly by mathematical evaluation via non-linear regression. Thus, several titration curves can be recorded simultaneously and transformed into a set of characteristic parameters, among them the dissociation constant and the concentration of binding-active receptor, and they can be evaluated statistically. When combined with this algorithm, titration ELISAs gain the advantage of directly presenting the dissociation constant. Therefore, they may be used more efficiently in the future.

After the ELISA has been developed, the yellow color of the converted alkaline phosphatase substrate, para-nitrophenolate, indicates that the amount of bound rhodocetin ligand decreases with decreasing concentrations of added rhodocetin from columns 1 to 11 (Figure 1). The colorless wells in the rhodocetin-free wells in column 12 show a low background signal.
Photometric quantification at 4...

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Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction

A detailed protocol to perform a titration ELISA is described. Moreover, a novel algorithm is presented to evaluate titration ELISAs and to obtain a dissociation constant of binding of a soluble ligand to a microtiter plate-immobilized receptor.

The dissociation constant describes the interaction between two partners in the binding equilibrium and is a measure of their affinity. It is a crucial ...

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Biochemistry

19.6K Views.  University of Münster. A detailed protocol to perform a titration ELISA is described. Moreover, a novel algorithm is presented to evaluate titration ELISAs and to obtain a dissociation constant of binding of a soluble ligand to a microtiter plate-immobilized receptor.

Video: Titration ELISA as a Method to Determine the Dissociation Constant of Receptor Ligand Interaction

Bio-layer Interferometry for Measuring Kinetics of Protein-protein Interactions and Allosteric Ligand Effects

We describe the use of Bio-layer Interferometry to study inhibitory interactions of subunit &#949;&#160;with the catalytic complex of Escherichia coli&#160;ATP synthase. Bacterial F-type ATP synthase is the target of a new, FDA-approved antibiotic to combat drug-resistant tuberculosis. Understanding bacteria-specific auto-inhibition of ATP synthase by the C-terminal domain of subunit &#949;&#160;could provide a new means to target the enzyme for discovery of antibacterial drugs. The C-terminal domain of &#949;&#160;undergoes a dramatic conformational change when the enzyme transitions between the active and inactive states, and catalytic-site ligands can influence which of &#949;&#39;s conformations is predominant. The assay measures kinetics of &#949;&#39;s binding/dissociation with the catalytic complex, and indirectly measures the shift of enzyme-bound &#949;&#160;to and from the apparently nondissociable inhibitory conformation. The Bio-layer Interferometry signal is not overly sensitive to solution composition, so it can also be used to monitor allosteric effects of catalytic-site ligands on &#949;&#39;s conformational changes.

The protocols here describe kinetic assays of protein-protein interactions with Bio-layer Interferometry. F-type ATP synthase, which is involved in cellular energy metabolism, can be inhibited by its &#949; subunit in bacteria. We have adapted Bio-layer Interferometry to study interactions of the catalytic complex with &#949;&#8217;s inhibitory C-terminal domain.

We describe the use of Bio-layer Interferometry to study inhibitory interactions of subunit &#949;&#160;with the catalytic complex of Escherichia ...

Chemistry

Measuring G-protein-coupled Receptor Signaling via Radio-labeled GTP Binding

G-Protein-Coupled Receptors (GPCRs) are a large family of transmembrane receptors that play critical roles in normal cellular physiology and constitute a major pharmacological target for multiple indications, including analgesia, blood pressure regulation, and the treatment of psychiatric disease. Upon ligand binding, GPCRs catalyze the activation of intracellular G-proteins by stimulating the incorporation of guanosine triphosphate (GTP). Activated G-proteins then stimulate signaling pathways that elicit cellular responses. GPCR signaling can be monitored by measuring the incorporation of a radiolabeled and non-hydrolyzable form of GTP, [35S]guanosine-5&#39;-O-(3-thio)triphosphate ([35S]GTP&#947;S), into G-proteins. Unlike other methods that assess more downstream signaling processes, [35S]GTP&#947;S binding measures a proximal event in GPCR signaling and, importantly, can distinguish agonists, antagonists, and inverse agonists. The present protocol outlines a sensitive and specific method for studying GPCR signaling using crude membrane preparations of an archetypal GPCR, the &#181;-opioid receptor (MOR1). Although alternative approaches to fractionate cells and tissues exist, many are cost-prohibitive, tedious, and/or require non-standard laboratory equipment. The present method provides a simple procedure that enriches functional crude membranes. After isolating MOR1, various pharmacological properties of its agonist, [D-Ala, N-MePhe, Gly-ol]-enkephalin (DAMGO), and antagonist, naloxone, were determined.

Guanosine triphosphate (GTP) binding is one of the earliest events in G-Protein-Coupled Receptor (GPCR) activation. This protocol describes how to pharmacologically characterize specific GPCR-ligand interactions by monitoring the binding of the radio-labeled GTP analog, [35S]guanosine-5&#39;-O-(3-thio)triphosphate ([35S]GTP&#947;S), in response to a ligand of interest.

G-Protein-Coupled Receptors (GPCRs) are a large family of transmembrane receptors that play critical roles in normal cellular physiology and constitute a ...

An ELISA Based Binding and Competition Method to Rapidly Determine Ligand-receptor Interactions

A comprehensive understanding of signaling pathways requires detailed knowledge regarding ligand-receptor interaction. This article describes two fast and reliable point-by-point protocols of enzyme-linked immunosorbent assays (ELISAs) for the investigation of ligand-receptor interactions: the direct ligand-receptor interaction assay (LRA) and the competition LRA. As a case study, the ELISA based analysis of the interaction between different lambda interferons (IFNLs) and the alpha subunit of their receptor (IL28RA) is presented: the direct LRA is used for the determination of dissociation constants (KD values) between receptor and IFN ligands, and the competition LRA for the determination of the inhibitory capacity of an oligopeptide, which was designed to compete with the IFNLs at their receptor binding site. Analytical steps to estimate KD and half maximal inhibitory concentration (IC50) values are described. Finally, the discussion highlights advantages and disadvantages of the presented method and how the results enable a better molecular understanding of ligand-receptor interactions.

The presented protocols describe two enzyme-linked immunosorbent assay (ELISA) based techniques for the rapid investigation of ligand-receptor interactions: The first assay allows the determination of dissociation constant between ligand and receptor. The second assay enables a rapid screening of blocking peptides for ligand-receptor interactions.

A comprehensive understanding of signaling pathways requires detailed knowledge regarding ligand-receptor interaction. This article describes two fast and ...

Optimized Methods for the Surface Immobilization of Collagens and Collagen Binding Assays

Fibrosis occurs in various tissues as a reparative response to injury or damage. If excessive, however, fibrosis can lead to tissue scarring and organ failure, which is associated with high morbidity and mortality. Collagen is a key driver of fibrosis, with type I and type III collagen being the primary types involved in many fibrotic diseases. Unlike conventional protocols used to immobilize other proteins (e.g., elastin, albumin, fibronectin, etc.), comprehensive protocols to reproducibly immobilize different types of collagens in order to produce stable coatings are not readily available. Immobilizing collagen is surprisingly challenging because multiple experimental conditions may affect the efficiency of immobilization, including the type of collagen, the pH, the temperature, and the type of microplate used. Here, a detailed protocol to reproducibly immobilize and quantify type I and III collagens resulting in&#160;stable and reproducible gels/films is provided. Furthermore, this work demonstrates how to perform, analyze, and interpret in vitro time-resolved fluorescence binding studies to investigate the interactions between collagens and candidate collagen-binding compounds (e.g., a peptide conjugated to a metal chelate carrying, for example, europium [Eu(III)]). Such an approach can be universally applied to various biomedical applications, including&#160;the field of molecular imaging to develop targeted imaging probes, drug development, cell toxicity studies, cell proliferation studies, and immunoassays.

This work presents an optimized protocol to reproducibly immobilize and quantify type I and III collagen onto microplates, followed by an improved in vitro binding assay protocol to study collagen-compound interactions using a time-resolved fluorescence method. The subsequent step-by-step data analysis and data interpretation are provided.

Fibrosis occurs in various tissues as a reparative response to injury or damage. If excessive, however, fibrosis can lead to tissue scarring and organ ...

Isothermal Titration Calorimetry for Measuring Macromolecule-Ligand Affinity

Isothermal titration calorimetry (ITC) is a useful tool for understanding the complete thermodynamic picture of a binding reaction. In biological sciences, macromolecular interactions are essential in understanding the machinery of the cell. Experimental conditions, such as buffer and temperature, can be tailored to the particular binding system being studied. However, careful planning is needed since certain ligand and macromolecule concentration ranges are necessary to obtain useful data. Concentrations of the macromolecule and ligand need to be accurately determined for reliable results. Care also needs to be taken when preparing the samples as impurities can significantly affect the experiment. When ITC experiments, along with controls, are performed properly, useful binding information, such as the stoichiometry, affinity and enthalpy, are obtained. By running additional experiments under different buffer or temperature conditions, more detailed information can be obtained about the system. A protocol for the basic setup of an ITC experiment is given.

A general protocol for the use of isothermal titration calorimetry to monitor the binding thermodynamics for biological systems with moderate binding affinities is presented.

Isothermal titration calorimetry (ITC) is a useful tool for understanding the complete thermodynamic picture of a binding reaction.  In biological ...

Biology

Autoradiography as a Simple and Powerful Method for Visualization and Characterization of Pharmacological Targets

In vitro autoradiography aims to visualize the anatomical distribution of a protein of interest in tissue from experimental animals as well as humans. The method is based on the specific binding of a radioligand to its biological target. Therefore, frozen tissue sections are incubated with radioligand solution, and the binding to the target is subsequently localized by the detection of radioactive decay, for example, by using photosensitive film or phosphor imaging plates. Resulting digital autoradiograms display remarkable spatial resolution, which enables quantification and localization of radioligand binding in distinct anatomical structures. Moreover, quantification allows for the pharmacological characterization of ligand affinity by means of dissociation constants (Kd), inhibition constants (Ki) as well as the density of binding sites (Bmax) in selected tissues. Thus, the method provides information about both target localization and ligand selectivity. Here, the technique is exemplified with autoradiographic characterization of the high-affinity &#947;-hydroxybutyric acid (GHB) binding sites in mammalian brain tissue, with special emphasis on methodological considerations regarding the binding assay parameters, the choice of the radioligand and the detection method.

The method of autoradiography is routinely used to study binding of radioligands to tissue sections for determination of qualitative or quantitative pharmacology.

In vitro autoradiography aims to visualize the anatomical distribution of a protein of interest in tissue from experimental animals as well as humans. The ...

Neuroscience

Determination of Protein-ligand Interactions Using Differential Scanning Fluorimetry

A wide range of methods are currently available for determining the dissociation constant between a protein and interacting small molecules. However, most of these require access to specialist equipment, and often require a degree of expertise to effectively establish reliable experiments and analyze data. Differential scanning fluorimetry (DSF) is being increasingly used as a robust method for initial screening of proteins for interacting small molecules, either for identifying physiological partners or for hit discovery. This technique has the advantage that it requires only a PCR machine suitable for quantitative PCR, and so suitable instrumentation is available in most institutions; an excellent range of protocols are already available; and there are strong precedents in the literature for multiple uses of the method. Past work has proposed several means of calculating dissociation constants from DSF data, but these are mathematically demanding. Here, we demonstrate a method for estimating dissociation constants from a moderate amount of DSF experimental data. These data can typically be collected and analyzed within a single day. We demonstrate how different models can be used to fit data collected from simple binding events, and where cooperative binding or independent binding sites are present. Finally, we present an example of data analysis in a case where standard models do not apply. These methods are illustrated with data collected on commercially available control proteins, and two proteins from our research program. Overall, our method provides a straightforward way for researchers to rapidly gain further insight into protein-ligand interactions using DSF.

Differential scanning fluorimetry is a widely used method for screening libraries of small molecules for interactions with proteins. Here, we present a straightforward method to extend these analyses to provide an estimate of the dissociation constant between a small molecule and its protein partner.

A wide range of methods are currently available for determining the dissociation constant between a protein and interacting small molecules. However, most ...

Real Time Measurements of Membrane Protein:Receptor Interactions Using Surface Plasmon Resonance (SPR)

Protein-protein interactions are pivotal to most, if not all, physiological processes, and understanding the nature of such interactions is a central step in biological research. Surface Plasmon Resonance (SPR) is a sensitive detection technique for label-free study of bio-molecular interactions in real time. In a typical SPR experiment, one component (usually a protein, termed 'ligand') is immobilized onto a sensor chip surface, while the other (the 'analyte') is free in solution and is injected over the surface. Association and dissociation of the analyte from the ligand are measured and plotted in real time on a graph called a sensogram, from which pre-equilibrium and equilibrium data is derived. Being label-free, consuming low amounts of material, and providing pre-equilibrium kinetic data, often makes SPR the method of choice when studying dynamics of protein interactions. However, one has to keep in mind that due to the method's high sensitivity, the data obtained needs to be carefully analyzed, and supported by other biochemical methods. 
SPR is particularly suitable for studying membrane proteins since it consumes small amounts of purified material, and is compatible with lipids and detergents. This protocol describes an SPR experiment characterizing the kinetic properties of the interaction between a membrane protein (an ABC transporter) and a soluble protein (the transporter's cognate substrate binding protein).

Real Time Measurements of Membrane Protein:Receptor Interactions Using Surface Plasmon Resonance SPR

Surface Plasmon Resonance (SPR) is a label-free method for detecting bio-molecular interactions in real time. Herein, a protocol for a membrane protein:receptor interaction experiment is described, while discussing the pros and cons of the technique.

Protein-protein interactions are pivotal to most, if not all, physiological processes, and  understanding the nature of such interactions is a central ...

Competitive Binding Assay to Identify Compounds Disrupting Receptor-Ligand Interactions

Source: Schoofs, G., et al. <a href="https://appjove.unicartagenaproxy.elogim.com/v/57271">A Flow Cytometry-based Assay to Identify Compounds That Disrupt Binding of Fluorescently-labeled CXC Chemokine Ligand 12 to CXC Chemokine Receptor 4.</a> J. Vis. Exp. (2018).
In this video, we describe a flow cytometry-based competitive binding assay to detect the interactions between the CXC Chemokine Receptor 4 (CXCR4) and its fluorescently-labeled natural ligand CXC Chemokine Ligand 12 (CXCL12), in the presence of a CXCR4-targeting small molecule. Incubating CXCR4-expressing cells with lower small molecule concentrations allows CXCR4-CXCL12 binding to some extent, which progressively declines upon a gradual increase in small molecule concentrations.

Konkurencyjny test wiązania w celu identyfikacji związków zakłócających interakcje receptor-ligand

Source: Schoofs, G., et al. A Flow Cytometry-based Assay to Identify Compounds That Disrupt Binding of Fluorescently-labeled CXC Chemokine Ligand 12 to ...

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Biological Techniques

Biomolecular Interaction Detection Techniques

Protein-protein interactions

ELISA-Based Reporter Assay to Study the Receptor-Ligand Interaction in BW Cells

Source: Elias, S. et al., <a href="https://appjove.unicartagenaproxy.elogim.com/v/58685">A BW Reporter System for Studying Receptor-Ligand Interactions.</a> J. Vis. Exp. (2019)
This video demonstrates the reporter assay-based detection of the receptor-ligand interaction. The successful receptor-ligand interaction activates the downstream signaling pathway, causing the generation and release of cytokines as secretory reporter molecules in the solution, which is confirmed using ELISA.