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 ...

<ol>
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M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ligand-receptor+complexes:+origin+and+development+of+the+concept.">Ligand-receptor complexes: origin and development of the concept.</a> J Biol Chem. 279 (1), 1-12 (2004).</li><li>Bisswanger, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Ch.+1:+Multiple+Equilibria,+Principles+and+Derivations.">Ch. 1: Multiple Equilibria, Principles and Derivations.</a> Enzyme Kinetics: Principles and Methods. , 1-26 (2017).</li><li>Shimura, K., Kasai, K. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Affinity+gel+titration:+quantitative+analysis+of+the+binding+equilibrium+between+immobilized+protein+and+free+ligand+by+a+continuous+titration+procedure.">Affinity gel titration: quantitative analysis of the binding equilibrium between immobilized protein and free ligand by a continuous titration procedure.</a> Anal Biochem. 149 (2), 369-378 (1985).</li><li>Gong, M., Nikcevic, I., Wehmeyer, K. 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A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+Langmuir+isotherm:+a+commonly+applied+but+misleading+approach+for+the+analysis+of+protein+adsorption+behavior.">The Langmuir isotherm: a commonly applied but misleading approach for the analysis of protein adsorption behavior.</a> J Biomed Mater Res A. 103 (3), 949-958 (2015).</li><li>Stockell, A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+binding+of+diphosphopyridine+nucleotide+by+yeast+glyceraldehyde-3-phosphate+dehydrogenase.">The binding of diphosphopyridine nucleotide by yeast glyceraldehyde-3-phosphate dehydrogenase.</a> J Biol Chem. 234 (5), 1286-1292 (1959).</li><li>Heyn, M. P., Weischet, W. 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V., Springer, T. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Structural+basis+of+integrin+regulation+and+signaling.">Structural basis of integrin regulation and signaling.</a> Annu Rev Immunol. 25, 619-647 (2007).</li><li>Luo, B. H., Springer, T. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Integrin+structures+and+conformational+signaling.">Integrin structures and conformational signaling.</a> Curr Opin Cell Biol. 18 (5), 579-586 (2006).</li><li>Ricard-Blum, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+collagen+family.">The collagen family.</a> Cold Spring Harb Perspect Biol. 3 (1), a004978 (2011).</li><li>Eble, J. A., Tuckwell, D. S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+&#945;2&#946;1+integrin+inhibitor+rhodocetin+binds+to+the+A-domain+of+the+integrin+&#945;2+subunit+proximal+to+the+collagen-binding+site.">The &#945;2&#946;1 integrin inhibitor rhodocetin binds to the A-domain of the integrin &#945;2 subunit proximal to the collagen-binding site.</a> Biochem J. 376 (Pt 1), 77-85 (2003).</li><li>Eble, J. A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+&#945;2&#946;1+integrin-specific+antagonist+rhodocetin+is+a+cruciform,+heterotetrameric+molecule.">The &#945;2&#946;1 integrin-specific antagonist rhodocetin is a cruciform, heterotetrameric molecule.</a> FASEB J. 23 (9), 2917-2927 (2009).</li><li>Eble, J. A., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Dramatic+and+concerted+conformational+changes+enable+rhodocetin+to+block+&#945;2&#946;1+integrin+selectively.">Dramatic and concerted conformational changes enable rhodocetin to block &#945;2&#946;1 integrin selectively.</a> PLoS Biol. 15 (7), e2001492 (2017).</li><li>Bracht, T., Figueiredo de Rezende, F., Stetefeld, J., Sorokin, L. M., Eble, J. A. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Monoclonal+antibodies+reveal+the+alteration+of+the+rhodocetin+structure+upon+&#945;2&#946;1+integrin+binding.">Monoclonal antibodies reveal the alteration of the rhodocetin structure upon &#945;2&#946;1 integrin binding.</a> Biochem J. 440 (1), 1-11 (2011).</li><li>Harlow, E., Lane, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Chapter+5:+Immunizations.">Chapter 5: Immunizations.</a> Antibodies, a laboratory manual. 5, 53-138 (1988).</li><li>Lu, D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Analyzing+interactions+between+SSB+and+proteins+by+the+use+of+fluorescence+anisotropy.">Analyzing interactions between SSB and proteins by the use of fluorescence anisotropy.</a> Methods Mol Biol. 922, 155-159 (2012).</li><li>Fielding, L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=NMR+methods+for+the+determination+of+protein-ligand+dissociation+constants.">NMR methods for the determination of protein-ligand dissociation constants.</a> Curr Top Med Chem. 3 (1), 39-53 (2003).</li><li>Leavitt, S., Freire, E. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Direct+measurement+of+protein+binding+energetics+by+isothermal+titration+calorimetry.">Direct measurement of protein binding energetics by isothermal titration calorimetry.</a> Curr Opin Struct Biol. 11 (5), 560-566 (2001).</li><li>McDonnell, J. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Surface+plasmon+resonance:+towards+an+understanding+of+the+mechanisms+of+biological+molecular+recognition.">Surface plasmon resonance: towards an understanding of the mechanisms of biological molecular recognition.</a> Curr Opin Chem Biol. 5 (5), 572-577 (2001).</li><li>Rich, R. L., Myszka, D. G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Advances+in+surface+plasmon+resonance+biosensor+analysis.">Advances in surface plasmon resonance biosensor analysis.</a> Curr Opin Biotechnol. 11 (1), 54-61 (2000).</li><li>Pesquero, N. 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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>MgCl2</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&#39;s lab</td>
			<td></td>
		</tr>
		<tr>
			<td>NiNTA superflow column&#160;</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 ...

The overall goal of this titration ELISA is to determine the affinity constant of two binding partners in a reproducible and efficient manner using a novel algorithm. This method can help answer key questions not only in the field of protein ligand interaction and receptor research but also in applied life sciences such as pharmaceutical research and pharmacology. The main advantage of this technique is that the affinity constant of a receptor ligand interaction can be determined easily by titrating a receptor with a ligand on an ELISA plate and by using a novel evaluation algorithm.Begin this procedure by diluting the stock solution of Integrin Alpha 2 A Domain to a final concentration of five micrograms per milliliter in TBS magnesium chloride buffer. Both a wild type and a mutant Integrin Alpha 2 A Domain will be used in this demonstration. Fill each well of a row on a half area microtiter plate with 50 microliters of the Integrin Alpha 2 A Domain coating solution.Perform every titration row at least in duplicates. In this example, every titration row is performed in quadruplets. Seal the plate with foil and leave the plate at four degrees Celsius overnight.On the following day, remove the coating solution and fill each well with 15 microliters of TBS magnesium chloride buffer. Remove the wash solution and fill the wells with new wash solution. The washes will remove soluble receptor molecules which have not been immobilized to the plastic surface by physical absorption.The next step is to block non-specific binding sites by adding 50 microliters of one percent BSA solution in TBS magnesium chloride buffer to each well. Reseal the plate and incubate at room temperature for one hour. While the wells of the microtiter plate are being blocked with BSA, prepare a serial dilution of the ligand Rhodocetin.A start concentration of 243 enamel-eroded Rhodocetin and a dilution factor of 2.3 are used in this case. For the eight titration curves in this experiment, prepare 920 microliters of Rhodocetin solution at the highest concentration in one per cent BSA in TBS magnesium chloride in test tube number one. Pipette 520 microliters of one per cent BSA solution in TBS magnesium chloride into each of the other ten test tubes labeled two through eleven.Transfer 400 microliters of the Rhodocetin solution from test tube to test tube two. Mix both solutions by chut-ter-a-tion and then transfer 400 microliters from this mixture to test tube three. Continue this serial dilution until test tube eleven.For the success of this procedure, it is important to always fill every well quickly with solution to make sure the wells do not dry out. At the completion of the one hour incubation, remove the blocking solution from the microtiter plate wells. Immediately add 50 microliters of the Rhodocetin solution from test tube one into the wells of column one, the solution from test tube two to the wells of column two, and continue through column eleven.Add 50 microliters of one per cent BSA and TBS magnesium chloride as a ligand-free control to the wells of column twelve. Reseal the plate and incubate at room temperature for one and a half hours. To remove non-bound ligand molecules, remove the binding solution and fill each well with 50 microliters of HBS magnesium chloride buffer.Then remove the HBS buffer and add new HBS buffer. To chemically fix the receptor and bound ligand, fill each well of the microtiter plate with 50 microliters of a 2.5 per cent glutaraldehyde solution in HBS magnesium chloride buffer. Incubate the microtiter plate at room temperature for ten minutes.Remove and in inactivate excess glutaraldehyde by removing the fixation solution and filling each well with 50 microliters of TBS magnesium chloride buffer. Remove the wash buffer and add new wash buffer to each well. To begin this assay, remove the wash buffer from all wells of the microtiter plate and add to each well 50 microliters of the primary antibody solution, diluted one to two thousand in one per cent BSA TBS magnesium chloride.Reseal the plate and incubate it at room temperature. Remove the primary antibody solution from all wells and add to each well 50 microliters of TBS magnesium chloride buffer. Wash three times with TBS magnesium chloride buffer.Next, add to each well 50 microliters of the secondary antibody solution, diluted one to two thousand in one per cent BSA in TBS magnesium chloride. Reseal the plate, and leave it standing at room temperature. Remove the secondary antibody solution from the wells, and add to each well 50 microliters of TBS magnesium chloride buffer.Wash three times. After the third wash, tap the microtiter plate onto a tissue cloth to remove all traces of liquid. Using a multi-channel pipette, promptly add 50 microliters of the alkaline phosphatase detecting solution to each well of the microtiter plate to start the enzymatic conversion as simultaneously as possible.Incubate the plate at room temperature until the solution in the wells with the highest ligand concentration turns yellow. Depending on signal intensity, the incubation time may vary between five minutes and one hour. Stop the conversion of the phosphatase substrate by using a multi-channel pipette to add 50 microliters of a 1.5 molar sodium hydroxide solution to each well in the same order of the alkaline phosphatase detecting solution was added.Leave the plate for several minutes to ensure streak-free mixing of both solutions. Measure the optical density at 405 nanometers of each well using an ELISA reader. Start the data analysis by opening the table of raw data.Copy the columns from the Excel file, open Graph Pad Prism Five, open a new project file in the Main Menu and under new data and graph, choose the X Y format. Choose the option Enter and Plot a Single Point for each value for the Y axis and paste them into the data sheet of Graph Pad Prism as X and y values respectively. Transpose the optical density at 405 nanometer values into a column format.In the data sheet, the first column represents the concentrations as added ligand as X values, while the columns to the right contain the signal values of the eight titration curves as Y values. As a semi-logarithmic plot will be drawn, the last row, which counts the signals of the ligand-free controls, concentration zero, is deleted. Graph Pad Prism draws the plot which is seen in the graph section.For the X axis, a semi-logarithmic scaling is selected. The X axis shows the signal values measured as OD values at 405 nanometers. By double-clicking any of the symbols, they can be selected and marked by simple shape and color.The titration values for the wild-type form are highlighted with circles in different red shadings, whereas the titration signals for the mutant form are marked with blue squares. Open the analysis sub-program and under X Y Analysis, choose the option Non-linear Regression and press the New button to create a new equation. Type the titration curve equation into the newly opened template sheet and define the appropriate constraints.Analyze the values of the data sheet by choosing the newly created user-defined equation. Open the table with the calculated approximation values, which are shown under the results section on the left side of the software screen. In this representative microtiter plate for a Titration ELISA, the yellow color of the converted alkaline phosphatase substrate indicates that the amount of bound-ward ascetant ligand decreases with decreasing concentrations of added Rhodocetin.The lack of color in the Rhodocetin-free wells indicates a low background signal. A novel algorithm processes the raw data from photometric quantification at 405 nanometers to calculate the signal as a function of the total concentration of added Rhodocetin. The four titration curves for each receptor form while type and mutant are highly reproducible and almost superpose each other.In contrast, the two groups of titration curves are clearly separated from each other. The titration curves of the mutant alpha 2 A domain are shifted to higher Rhodocetin concentrations, indicating that Rhodocetin binds with lower affinity to the mutated receptor. The dissociation constants of the eight titration curves were plotted and grouped for the wild type and mutant form of the alpha 2 A domain.The affinity constant for the binding of Rhodocetin to the wild type alpha 2 A domain is 5.80 plus or minus 0.15 nanomolar, whereas Rhodocetin binds to the mutated receptor with a significantly lower affinity of 9.68 plus or minus 0.18 nanomolar. Once optimized for routine, this technique can be done within six to seven hours. While attempting this procedure, it is important to remember that the glutaraldehyde might affect ligand binding to the receptor and might harm the epitopes of the ligand, thereby compromising antibody detection.This must be tested beforehand. If the equipment for surface plasma resonance is available, the SPR method could be used as an alternative, however, SPR evaluates kinetics data to determine the affinity constant. This Titration ELISA in combination with the novel evaluation algorithm is versatile and can, for instance, be used to compare the affinities of different ligands to analyze structure activity relations and to unravel the molecule mechanism of protein-ligand interactions.After watching this video, you should have a good understand of how to perform the Titration ELISA and how to implement this novel evaluation algorithm so that the affinity constant for any protein-ligand interaction can be determined easily and routinely, even for multiple ligands simultaneously. Don't forget that working with glutaraldehyde can be hazardous. Therefore, safety measures such as wearing gloves and goggles should always be taken while performing the fixation step of this protocol.

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Research

JoVE Journal

Biochemistry

19.4K Views.  University of Münster. The overall goal of this titration ELISA is to determine the affinity constant of two binding partners in a reproducible and efficient manner using a novel algorithm. This method can help answer key questions not only in the field of protein ligand interaction and receptor research but also in applied life sciences such as pharmaceutical research and pharmacology. The main advantage of this technique is that the affinity constant of a receptor ligand interaction can be determined easily by ti...