Validation of the fitting results is an essential step. Do not believe the calculated values without checking! Always inspect the curves and residuals. In addition, inspect the calculated values (Rmax, RI, Req, ka, kd). Do they make sense?
The best way to see if a fitting follows the measured data is by visual inspection (1), (2). Deviations of the fitting from the actual data are easily found by inspection of the residuals. Discrepancies between the fitted model and the experimental data are of two kinds (3):
The random deviations should reflect normal scatter in the experimental data. This kind of deviation should have a normal distribution meaning that high and low deviations are occurring at the same amount.
The systematic deviations arise because the model is an inadequate description of the experimental situation. The association or dissociation is faster or slower or the calculated RI jump is smaller. By careful inspection of the deviation, you can get clues about what is the cause of the deviation.
Examine the Chi2-values and the residual plots for the fitting. Points in the residual plot are scattered within a band. The width of the band at a given time indicates the noise level, while the shape of the band reveals systematic differences between the fitted curve and the experimental data (4), (5). For typical sensorgrams, the noise level should not exceed the normal noise level of the instrument. In the global analyses, the noise level may be somewhat higher. Time to 5% dissociation
Start by inspecting the kd. In order to have a valid calculation the dissociation should be at least 5% of the starting value. If the value is lower than 1.10-5 s-1 the dissociation time should be at least 90 minutes (see table). The ka should be in the valid range of the instrument. In addition, are the calculated variables biologically relevant?
The Rmax is also calculated during the fit. The Rmax reflects the maximal response when all ligand is occupied. This will be hardly the case, even if you inject a 100 times the KD. In addition, the time needed to reach Rmax (at Req) can be beyond the injection time of the instrument. Use the Rmax and Req to judge if the curves following a 1:1 kinetic. If the Rmax is very high compared to the response of the curves this can be an indication that the fit is wrong.
|Instrument||ka (M-1s-1)||kd (s-1)||KD (M)|
|Biacore 2000||103 – 5.106||5.10-6 – 10-1||10-4 – 2.10-10|
|Biacore 3000||103 – 107||5.10-6 – 10-1||10-4 – 2.10-10|
|Biacore X100||103 – 107||1.10-5 – 10-1||10-4 – 1.10-10|
|SensiQ Pioneer||< 108||1.10-6 – 10-1||10-3 – 10-12|
|IBIS-MX96||10-5 – 10-12|
|Plexera HT analyzer||102 – 106||10-2 – 10-5||10-6 – 10-9|
|Reichert SR7500DC||10-3 – 10-9|
|SierraSensors SPR-2||103 – 106||10-1 – 10-5||10-4 – 10-11|
How is the standard error (SE)? (6). The standard error of the calculated values is often very low, indicating that the value is well defined. Do not use the standard error in the reporting of your values. If you want to report an error to your values, you have to repeat the experiment and calculate the standard deviation (check Wikipedia).
The Chi2 shows also information about the goodness of fit but is less affected by the large number of data points. However, the Chi2 is difficult to interpret (8). First, it depends strongly on the average signal level and therefore a generally acceptable Chi2 cut-off cannot be established. Second, it is not well adapted for time series data, because there is typically a strong correlation between data points in close temporal proximity. However, the Chi2 can be used as a global measure for the residual noise. For a good fitting, the square root of Chi2 is of the same magnitude as the noise of the measurement.
In the cases that the fitting is not optimal, you can use another model. However, this model surfing will not give you any better understanding of what is happing during the interaction. Instead of applying various models to measured curves, try to design proper experiments. So:
Examine the results for consistency over a range of analyte concentrations. In the global analysis method, this is performed in the fitting procedure. Nevertheless, inspect each of the fitted curves for deviations. When fitting one curve at the time, check if the constants vary with the analyte concentration. If so, the model is probably inadequate.
Some simple test can be done to check if the reported values are consistent (7). The calculated KD value obtained from the equilibrium reaction must be the same as the KD calculated from de individual ka and kd values from the association phase.
The calculated (fitted) kd from the association phase must approximately be the same as from the dissociation phase.
The calculated (fitted) observed rate constant (kobs) in the association phase must comply with the next two conditions. Beware that the evaluation software the kobs calculates from ka, C and kd.
The next list contains references that are very interesting to read. So I suggest you look them up and study.
|1.||Cornish-Bowden, A.; Detection of errors of interpretation in experiments in enzyme kinetics; Methods ;24: 181-190; (2001).|
|2.||kalinin, N. L. et all ; Effects of solute multivalence on the evaluation of binding constants by biosensor technology: studies with concanavalin A and interleukin-6 as partitioning proteins; Analytical Biochemistry ;228: 238-244; (1-7-1995).|
|3.||Roden, L. D. and Myszka, D. G.; Global analysis of a macromolecular interaction measured on BIAcore; Biochem.Biophys.Res.Commun. ;225: 1073-1077; (23-8-1996).|
|4.||Wu, Z. et all ; Ligand binding analysis of soluble interleukin-2 receptor complexes by surface plasmon resonance; J.Biol.Chem. ;270: 16045-16051; (7-7-1995)|
|(1)||Morton, T. A. et al; Interpreting complex binding kinetics from optical biosensors: a comparison of analysis by linearization, the integrated rate equation, and numerical integration. Analytical Biochemistry227: 176-185; (1995).|
|(2)||Cornish-Bowden, A.; Detection of errors of interpretation in experiments in enzyme kinetics. Methods24: 181-190; (2001). Goto reference|
|(3)||BIACORE AB; BiaEvaluation 2.0. (1998).|
|(4)||De Crescenzo, G. et al; Real-Time Kinetic Studies on the Interaction of Transforming Growth Factor alpha with the Epidermal Growth Factor Receptor Extracellular Domain Reveal a Conformational Change Model. Biochemistry39: 9466-9476; (2000).|
|(5)||Onell, A. and Andersson, K.; Kinetic determinations of molecular interactions using Biacore - minimum data requirements for efficient experimemtal design. J.Mol.Recognit.18: 307-317; (2005).|
|(6)||BIACORE AB; Kinetic and affinity analysis using BIA - Level 1. (1997).|
|(7)||Schuck, P. and Minton, A. P.; Kinetic analysis of biosensor data: elementary test of self-consistency. Trends Biochem.Sci.21: 458-460; (1996).|
|(8)||Onell, A. and Andersson, K.; Kinetic determinations of molecular interactions using Biacore - minimum data requirements for efficient experimemtal design. J.Mol.Recognit.J.Mol.Recognit. (18): 307-317; 2005.|