Experimental tests of the quantitative model.

To test the model of the previous section, we performed several experiments to genotype DNA for the presence of a homozygous or heterozygous SNP, 187C>G, which is found in the hemochromatosis gene (HFE). This mutation we analyzed 
5'-TCA-3'  ->  5'-TGA-3'
3'-AGT-5'       3'-ACT-5'
has the nearest-neighbor symmetry described above which results in a melting curve for the homozygous case which is theoretically identical to and experimentally indistinguishable from that of wild-type DNA.
(See figure ? for the complete sequence with SNP and primers highlighted.
H63D_sequence_031010.doc)

We chose to examine a range of 21 different ratios of wild-type spike to
spike plus unknown, from 1/28 to 14/28 by increments of 1/28, and from
15/28 to 27/28 in steps of 2/28. This allowed us to include the theoretically optimal
value, 1/7, and observe the behavior of the process in some detail over a wide
range of interest for pooled samples as well. The ratio j/28 of spike to spike plus
unknown corresponds to the ratio j/(28-j) of spike to unknown, so for instance,
the optimal value of 4/28 is the same as 4/24=1/6 spike to unknown.

We spiked three replicates of each of the three genotypes (denoted WT, MUT, and HET) before PCR with each fraction of additional wild-type DNA. 
Samples with a common spike fraction as well as two control samples containing  unspiked heterozygous DNA were amplified in the presence of a high-resolution fluorescent dye and analyzed simultaneously.

The PCR protocols may be found in appendix ? (Michael)

Following amplification, an additional melting was performed to denature the perfectly complementary post-extension duplexes after which the temperature was rapidly decreased to re-anneal strands independent of the presence or absence of a single mismatched base-pair. 

We then performed high-resolution melting analysis on all of the resulting samples to produce actual fluorescence vs. temperature melting curves corresponding to the model of the previous section. This is a closed-tube process which avoids risk of contamination and leaves the sample undisturbed for further types of analysis.
It provides a fast, economical, and accurate method of genotyping and mutation scanning which has been described and studied in a variety of contexts ([ ],[ ],...,[ ])
(Carl)

After high-resolution melting analysis, we performed temperature-gradient capillary electrophoresis (TGCE) on each sample. In this technique, we detect the arrival of duplexes in a sample after they are drawn through a gel. Each species of duplex has a characteristic arrival frequency distribution depending on its spatial conformation. In particular, the center of a heteroduplex arrival frequency peak is significantly delayed due to the "bubble" formed by mismatched base pairs. While the two species of homoduplex have arrival frequency peaks which superpose indistinguishably, the two heteroduplex peaks are easily separated from the homoduplex peak and from each other. The peaks exhibit simple mathematical behavior which makes it possible to separate and quantify the relative contributions of the heteroduplexes. This provides an independent and direct validation of our theoretical model of melting curve separation, which was based upon relative
concentration of heteroduplexes in the samples.

The mathematical analysis of the data from these two methods is discussed in the next section.

--------------------------------

Analysis of experimental data and comparison with the theory. (Outline)

--------------------------------


Analysis of melting curve data:

Background removal (line or new method - not much difference, so should
we stick with line method or describe new method?) 

Temperature shift
uses features of the background removed curves themselves to compensate
for small variations in temperature control - reported vs. actual temperature.

Difference plots highlight relative variation between genotypes

According to the theory, location of maximum difference is constant, and magnitude of maximum difference, and area under difference are directly proportional to the heteroduplex concentration of the samples. 

Figure ? and Table ? in the appendix show the calculated values of the
maximum difference and area between the average of three replicate spiked wild-type melting curves and the individual spiked homozygous and heterozygous SNP melting curves as a function of the proportion of the spike in the total mixture. The values are normalized to make the value of an unspiked heterozygote equal to .5,
to correspond to the concentration of heteroduplexes in the theoretical model, which is superimposed on the figures. (The differences between the homozygous and heterozygous replicates is implicit, and can be obtained by taking the difference of their individual differences with the mean wild-type curve, as in the theoretical analysis.) The location of the maximum differences is reported in Table ?

---------------------------------


Analysis of TGCE data

Individual TGCE arrival frequency peaks may be approximated by exponential distributions of the form F(t)=Ae^{-kt}, t >=t_0; F(t)=0, t<t_0. Higher resolution data might be amenable to closer fit by higher order gamma distributions of which the exponential distribution is a special case, but since the peaks are only resolved by on the order of 10 data points, the simplest version must suffice. Some additional evidence that this is reasonable is provided by the fact that the fit parameters of each peak remained nearly invariant when the window of points
used for the fit was varied in size and distance from the peak. The observed arrival frequency before each peak did not have the strict cutoff behavior of the exponential distribution, as some increase above background was seen one frame before the maximum of the first arrival peak. However, no increase above background could be seen two frames before the first arrival peak. Based upon this model, we could solve for the combined amplitudes and decay rate of homoduplex concentrations contributing to the first arrival peak, and by successive subtraction, iteratively solve for the amplitudes of subsequent peaks. It is interesting to note that both by scaling of the subtracted data of different peaks and by independent
fitting, the decay rates of different peaks were nearly independent of species and
amplitude. Because of the large dynamic range of the peaks and their narrow extent in terms of data acquisition frames, the quantitative results are somewhat sensitive to the fitting process. In particular, we have identified the start of each exponential sub-distribution with the maximum measured value, even though this value might easily be sampled after, or even before the true peak. We are investigating more sophisticated gamma fits of the data, along with corresponding deconvolution techniques which could reduce these sources of error. However, the agreement reported below between the results of even the more simplified approach and those of the melting curve experiments and the theory suggest that  quantitative TGCE (QTGCE) estimation of heteroduplex content of spiked or pooled samples is indeed feasible.


------------------------------------------------

Discussion of the results:


The results confirm the main points of the theory to a considerable degree of accuracy. The location of the maximum difference between curves is effectively independent of the spike proportion. The maximum difference between curves data and the area between curves data agree with each other, with the heteroduplex concentrations inferred from TGCE experiments and analysis, and  with the theoretical predictions of heteroduplex concentration over a wide range of spiking proportions. 

All of the scatter plots follow the quadratic behavior of the model qualitatively over the entire range, and are quantitatively close over a range of spike proportions up to one-half (14/28) of the total.

Where the data deviates from the model above this spiking value, there is a definite trend for heteroduplex concentrations estimated from TGCE and corresponding melting curve differences to be larger than those predicted by the theory for a given spike proportion. Not only do the overall melting curve and TGCE values follow each other, the individually labeled replicates have a high degree of correlation, both of which indicate that the measured values are indeed higher and not merely artifacts. Because the heteroduplex concentration vs. spike proportion curves for both the heterozygous and heterozygous unknowns are decreasing for spike proportions greater than 14/28, the inferred experimental values correspond to spike proportions lower than those we prepared experimentally. So one possible source of such a trend could be that the actual proportion of wild-type spike fell short of the intended value as that value grew beyond one-half.  Selective amplification (unequal efficiencies) in PCR or amplification of initial variations that diminish final concentration of wild-type spike at higher concentrations could have such an effect. Ways in which the experiments could deviate from the assumptions of the model include non-independent re-annealing of duplexes after the final post-extension melting, although it would be surprising if this favored formation of more heteroduplexes than would be produced by random association.

Regardless of the subtle deviations from otherwise close agreement with a quite simple model, the ultimate test of our method is given by the ease with which the simple melting curve approach to can be used to genotype the optimally spiked samples, in contrast to unspiked or non-optimally spiked ones.

In the final figure (?a), we show the normalized melting curves of three replicates of each of the three optimally spiked genotypes. The replicates cluster indistinguishably, appearing as one curve, and the three genotypes are plainly separated by the observer's eye or by our automatic classification  software.
This is a vast improvement from the initial figure in which replicates of the homozygous SNP and the wild-type samples overlapped each other completely,
and considerably better than even figure (?b) with samples spiked non-optimally with equal parts wild-type spike and sample or (?c) where 1/3 spike proportion makes the heterozygous and homozygous SNP samples overlap each other in both theory and experiment.