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Analysis of melting curves

Fig 4: Comparison of a derivative based method and the model based algorithm with the reference values for the melting temperature. The upper row gives the correlation between the derivative based method and the standard values, the lower  the model based algorithm.

 

The determination of the melting temperatures needs a high accuracy and reproducibility to improve upon the specificity achievable via mature endpoint microarrays. The starting point was a comparison of the derivative based method and the model based algorithm. Correlation of the two methods with manually adjusted reference values from standard Genewave normalization software are shown in figure 4. The model based values gives a better correlation than derivative based values. No improvement of Savitzky-Golay filtering in comparison to simple low-pass filtering was found. This might be due to the quite simple shape of the melting curve. For different hybridization experiments the parameters of Savitzky-Golay filtering had to be modified manually and there is no potential for reduction of experimental data acquisition. With the model based algorithm it was possible to reproduce the results of the standard software without any manual adjustment.

Fig 5: Normalized melting curves for RNA•RNA hybrids (left) and DNA•DNA duplexes (right).The normalized representation gives a good picture of the temperature behavior of the system. Crosses indicate experimental values, the lines indicate fit functions.

Figure 5 gives examples for the application of the algorithm to normalized melting curves. The temperature behavior of the different target systems (RNA•DNA hybrids and DNA•DNA duplexes) is according to the model. The normalized melting curves for short oligo systems and the fit functions are shown in Figure 6.  The quality of the description is comparable to that of long oligo systems.

Fig 6: Examples for RNA-DNA hybrids (left) and DNA-DNA duplexes (right)  for short oligo systems. Crosses indicate experimental data,  the lines are the fit functions.

To test the potential for inter- and extrapolation datasets with reduced number of data points were created as well. Fig. 7 gives a typical result. Only every third measurement point was used up to melting temperature. No experimental data above the melting temperature have been used. For this analysis a selection of probes with similar melting temperature has to be done. To take into account the remaining intensity of unspecific bound fluorophores at high temperatures the final intensity was set to 100 for all experiments. The algorithm gives a good prognosis to higher temperatures which could give another advantage of the algorithm for melting analysis. The higher the experimental temperature the lower is the signal to background ratio. The high potential in reduction in experimental data opens the door for cheaper and faster microarray based melting analysis. The good results for extrapolation suggest a fundamental relation between the melting of surface bound nucleic acids and  Fermi-Dirac statistics.

Fig. 7: Application of the algorithm to a reduced data set. The stars indicate data points used for algorithm. The solid line gives the fitted function, the points denote experimental values. For high temperatures the value of the fit function were  set to 100. For this representation a selection of probes based on the melting temperature was done and not normalized data were used for better visibility.

Another interesting opportunity of this algorithm is the automated detection of multiple target hybridization to a single spot. In endpoint based mutation screening the discrimination between different alleles in heterocygote samples and nonspecific hybridization of a single target is still challenging. In case of melting analysis the shape of the melting curve is changed due to the overlaid melting processes of the different targets. Thus for multiple target melting the parameter kb is smaller.

A histogram of the distribution of kb for single and multiple target hybridization is shown in Figure 8. The histogram is based on the results of 6 experiments and shows the robustness of this quality control parameter. With 60 mer probes the 2 mismatches yield a difference of about 4 °C for single target hybridization between the PM and the MM. In case of two targets the slope of the melting curve is decreased and the corresponding parameter kb is clearly shifted to smaller values. Thus automated discrimination between single and multiple target hybridization is possible.

Fig 8: Histogram of the parameter kB for single and multiple target hybridization. The right peak denotes the single target hybridization to the probe, the left a hybridization of a mixture of a perfect match and a 2MM target. The inset shows the normalized melting curves. Data are from 6 experiments.