Fig. 1: Application of the proposed algorithm to long (left) and short (right) oligo hybridization kinetics. The crosses are the experimental values, the lines give the results of the proposed algorithm. For the first hour the interval for the image acquisition was one min, afterwards 30 min.
The figure above gives an example of the application of the algorithm for long and short oligo microarrays. The proposed fit function gives a good representation of the kinetics for both types of nucleic acids. The kinetic behavior of long and short oligo hybridization kinetics can be described by the biexponential function with a very good accuracy. It is interesting to see that in spite of the effective agitation equilibrium was not reached after 18 hours for low target concentration of 0.5 nM. For higher target concentrations (3.6 nM) equilibrium was reached after about 5 hours without competitive hybridization. In case of competitive hybridization, where signal intensity decreases after a specific maximum, equilibrium was never reached during our experiments (up to 18 hours hybridization time). This is an interesting result indicating the limitations of endpoint microarray analysis. In case of closely related target mixtures there is a significant change of signal ratios after overnight hybridization.
One main focus of the development of the algorithm was to assess the potential for the reduction of experimental data acquisition. Reduced data sets were generated and used for fitting. The full data set was used for verification. The results for the theoretical limit of 3 experimental values and the initial point (0,0) is shown in figure 2. Even in this case the GoF is quite high, thus proving the validity of the model for a numerical description of nucleic acid hybridization kinetics.
Fig. 2: Application of the algorithm using only three datapoints, marked with stars, and the initial value (0,0). The points show all measured data, the fit is given by the solid line.
Obviously it is not possible to do an accurate quality control with this reduced data set without reference curves. Automated comparison of the kinetic parameters to reference measurement is a fast and simple quality control of the hybridization and for quantification of competitive hybridization in huge data sets. Due to the concentration dependency of competitive hybridization this can be used for quantification of target concentration.
Fig. 3: Histogram of CoD for kinetic analysis (top) and melting analysis (bottom). It is easy to set a threshold for quality monitoring. It is important to note the high value for the Coefficient of Determination (CoD).
This last figure gives a histogram of the quality parameter CoD. Low quality spots can be easily separated from the standard measurements. Some authors propose a more complex model with 3 species including low affinity background hybridization. Within our stringent experimental setup we did not see significant influence of unspecific background (salmon sperm DNA in 100x target concentration) nor the necessity for a more complex model even when using up to 8 closely related targets in similar concentration or in unspecific background (salmon sperm DNA 100x concentration). Nevertheless, it is important to note that it is not an analytical model for the complex hybridization and displacement reaction but a physical model based fitting algorithm.
