AUTOLAB APPLICATION NOTE Affinity constants from SPR equilibrium To test the binding capacity of the surface the analyte can be determined. It is always important to check analysis in a concentration of approximately 10 times the the quality of the fits! estimated binding constant is injected and the SPR Req as function of the free analyte concentration can Two ways to assay affinity constants for biomolecular signal at equilibrium assayed. Preferably this would be plotted (Fig. 2) and non-linearly fitted to a one-site interactions are described. Firstly, the affinity for an be in the range of 60 to 100 mº. If it is too low the binding isotherm (Eq. 1). immobilized ligand (KC), and secondly, affinity of the assay will be less accurate. If it is too high, the interaction in solution (KS), using SPR competition interaction can be slow, especially with low analyte [analyte] free experiments. Although affinity constants can be concentration; the correction for analyte depletion Req = .Rmax (1) (see below) can be large; and the effects of mass [analyte] + K derived from kinetic information, here the equilibrium transport will be more evident. free C signal is used, to avoid complications of mass transport limitation and the use of binding models that In the actual experiment solutions of analyte are made in a concentration range around the estimated With non-linear fitting programs (not our KE program) may not be appropriate for the system under readily available now, a non-linear fit is preferred over investigation.1 The cuvette design of the Autolab SPR KD value. Solutions of analyte are made in buffer e.g. HBS buffer pH 7.4. The highest concentration should a linear fit e.g. from a Scatchard plot. The fit yields is pre-eminently suitable to obtain the signal at values for KC and Rmax, the value of Req at saturation equilibrium. be approximately 5-10 times the estimated KD value, the lowest concentration at least equal to KD, but of binding. The species (a protein or other macromolecule) that is added in solution and binds to the immobilized preferably lower. However, at low concentrations it can take a long time before equilibrium is reached! Depletion correction ligand is defined as the analyte. In the cuvette-based ESPRIT instrument the For an interaction plot at least 5 data-points are needed. Sensorgrams of the analyte interactions are concentration of free analyte decreases due to Affinity of an analyte to an immobilized binding to the surface, for this a correction can be recorded (Fig. 1). From the sensorgrams the SPR ligand on the SPR sensor chip. made according to Eq. 2. 2 signal at equilibrium is determined. This is Req .S.10−9 After initialization of the SPR chip, the initial step is easily done with the [analyte free = [analyte total − ] ] (2) coupling of one of the reactants to the SPR chip (see Autolab kinetic 122.MWanalyte.Vbulk Application Note 31). The conditions can vary much software. Make an and depend amongst others on isoelectric point and overlay of the blank S of the standard sample cell is 2.6 mm2, Vbulk under the type of sensor chip. The following is based on corrected curves of standard conditions is 35 µL. MW is the molecular EDC/NHS as the coupling strategy. To allow interest, position the weight of the analyte. The effect of depletion complete access to the analyte-binding site, for small baseline at the start on correction is shown in ligands insertion of a spacer between the binding zero for all curves, and Fig. 2: without correction epitope and the sensor dextran matrix is advisable. fit a part of the (dotted line, open When a stable surface is needed covalent coupling is association phase symbols) KC in this preferred over non-covalent immobilization like including a part of the equilibrium signal, with the example is found to be biotin/avidin coupling. Following the standard monophasic association model. The equilibrium 8.0 nM, and with EDC/NHS procedure, as a rule of thumb one could signal (Req) is given by the fit parameters E+R(0). If correction (closed start with 1-2 mM ligand reacting during 5-10 min with equilibrium is not reached, e.g. for a low symbols, solid line) 5.5 the activated sensor surface (see Application note concentration (see Fig. 1), using this method also Req nM. The depletion 31). AUTOLAB ELECTROCHEMICAL INSTRUMENTS ARE DEVELOPED AND PRODUCED BY ECO CHEMIE B.V. IN THE NETHERLANDS appl032-1 www.ecochemie.nl. AUTOLAB APPLICATION NOTE correction can be readily calculated in a spread A − A 2 − 4[analyte] total .[ligand] total extremely flexible proteins if their conformational sheet. [analyte] free = [analyte] total − freedom is limited by binding to the sensor surface. 2 Deviations between KS and KC are also observed if Affinity of an analyte to a ligand in solution. not the proper value of the analyte concentration is in which A = [ K S ] + [analyte]total + [ligand ]total used. From SPR competition experiments the equilibrium The big advantage of this approach is that series of constant of a molecular interaction in solution (KS) Substitution of Eq. 4 into Eq. 1 gives the complete ligands can be investigated using the same sensor can be derived. KS is defined by Eq. 3. expression, which can be introduced into a non-linear surface, without preparing individual surfaces for fitting program. It should be noted that this every ligand. [analyte] free .[ligand ] free, solution expression contains KC, therefore the affinity to the KS = (3) sensor surface must be determined (section A of this References [analyte − ligand ]complex, solution Note). In the fit the numerical values of [analyte]total and KC is introduced, and the fit yields values for KS (1) Schuck, P.; Minton, A. P. Kinetic analysis of The experiments are and Rmax. biosensor data: elementary tests for self-consistency. performed with A few remarks concerning the application of this Trends Biochem Sci 1996, 21, 458-460. samples containing a approach: constant concentration If binding constants are not needed, and only the (2) de Mol, N. J.; Plomp, E.; Fischer, M. J. E.; of analyte in the relative affinity of ligands has to be established, from Ruijtenbeek, R. Kinetic analysis of the mass transport presence of a the inhibition curves IC50-values can be derived limited interaction between the tyrosine kinase lck concentration range of without fitting to the KS model. SH2 domain and a phosphorylated peptide studied ligand. Req determined The fixed analyte concentration in the competition by a new cuvette-based surface plasmon resonance from the sensorgrams experiments is best chosen as 1 to 4 times KC. instrument. Anal Biochem 2000, 279, 61-70. (see section A of this In the fit all concentrations should be in the same unit Note) is plotted as a (M, µM or nM). KS will be returned in that same (3) de Mol, N. J.; Gillies, M. B.; Fischer, M. J. E. function of the ligand concentration unit. Experimental and calculated shift in pK(a) upon concentration in solution (Fig. 3). In the presence of The returned value of Rmax is the value at complete binding of phosphotyrosine peptide to the SH2 competing ligand Req is determined by the affinity to saturation of all binding sites and should be domain of p56(lck). Bioorg Med Chem 2002, 10, the immobilized ligand and the amount and affinity of compatible with the value from the KC experiment. 1477-1482. the ligand in solution. The amount of sensor-bound Also in these experiments loading of the chip should analyte is again described by Eq. 1, but now the not be too high, as correction for depletion is not amount of free analyte is diminished by binding to the feasible here. For lower MW analytes one has to note ligand in solution. Based on this a modification of Eq. especially this point (compare Eq. 2) 1 can be derived which fits the data of Fig. 3 3. Here the expression of [analyte]free is given for the In general for a bimolecular interaction the values for competition conditions (Eq. 4). KC and KS are found to be similar. Deviations can be found for dimer interactions (e.g. GST-fusion (4) proteins), high MW analytes (MW >100 KDa) due to lower partition in the dextran layer of the sensor, and AUTOLAB ELECTROCHEMICAL INSTRUMENTS ARE DEVELOPED AND PRODUCED BY ECO CHEMIE B.V. IN THE NETHERLANDS appl032-2 www.ecochemie.nl.
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