Legends CTW - Department of Mathematics, University of Utah

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Figure 1. Melting curves of synthethized oligonucleotide homoduplexes, heteroduplexes and their mixture for an SNP with nearest neighbor symmetry.

Normalized melting curves of synthetic 40 bp homoduplexes and heteroduplexes are shown. The sequences of the duplexes are the same as the HFE H63D (187C>G) PCR products used in the rest of the study. Binary mixtures of strands with complementary bases (C:G or G:C) at the SNP form homoduplexes that have identical melting curves because of nearest neighbor symmetry. Strands with mismatched base pairs at the SNP form heteroduplexes with destabilized melting curves (C:C less stable than G:G). Equal parts of all strands were mixed and the resulting melting curve in the center resembles that of the genomic heterozygous sample after PCR amplification (see Fig. 2). The predicted heterozygote curve (dotted line) is the weighted average of the two homoduplex and two heteroduplex melting curves. The weighting for each duplex applied at each temperature is the fluorescence contribution from that duplex, divided by the fluorescence of all individual duplexes.

Figure 2. Melting curves of an SNP with nearest neighbor symmetry after PCR amplifcation.

The same sequence as in Fig. 1 was amplified from genomic DNA by PCR and melting curves were obtained for wild type (WT), mutant homozygous (MUT) and heterozygous (HET) genotypes. Three different DNA samples of each genotype are displayed. In panel A, normalized melting curves are displayed. All homozygous samples appear to trace the same path. Melting curves of heterozygous samples show a low temperature transition from the contribution of heteroduplexes, as predicted from

Fig. 1. In panel B, the difference of each curve from the mean wild type curve is displayed.

Figure 3. The dependence of heteroduplex proportion on genotype and the fraction of added wild type DNA.

When wild type reference DNA is mixed with homozygous mutant (MUT) or heterozygous (HET) DNA, the resultant heteroduplex proportion depends on the fraction of reference DNA (x) in the mixture. For homozygous mutant

DNA, the heteroduplex proportion is 2x(1-x), shown in the figure as a solid curve. For heterozygous DNA, the heteroduplex proportion is ½(1-x

2

), shown as a dashed curve.

The optimal separation between genotypes occurs when the reference DNA fraction is

1/7 (left vertical line), giving heteroduplex proportions of 0/49 (WT), 12/49 (MUT) and

24/49 (HET). When the reference DNA fraction is 1/3 (right vertical line), both MUT and HET samples have the same heterodupex proportion (4/9) and cannot be differentiated. Detailed derivations are provided as Supplementary Material.

Experimental high-resolution melting data for homozygous mutant (circles) and heterozygous (squares) samples are shown as the mean and standard deviation of three replicates. These values are the maximum fluorescence difference between the wild type melting curves and each mixture, scaled to make unmixed heterozygous samples equal to

0.5. This scaling allows for direct comparison to predicted heteroduplex proportions.

Figure 4. Melting curve analysis of an SNP with nearest neighbor symmetry after addition of an optimal amount of wild type DNA and PCR amplification.

Three samples of each genotype (WT = wild type, HET = heterozygous, MUT = homozygous

mutant) were mixed with wild type DNA to obtain a reference DNA fraction of 1/7.

After amplification, melting, and normalization, mutant homozygous curves were equidistant from the wild type curves and the barely altered heterozygous curves. All samples of the same genotype appear as single curves because of the high-resolution analysis. Individual curves can be seen in panel B where the difference of each curve with the mean wild type curve is displayed. The heterozygous and homozygous curves have the same shape and peak, while their magnitude varies by a factor of two, as predicted (Fig. 3). The heteroduplex content of the homozygous mutant mixture is 0.5 times that of the heterozygous mixture.

Figure 5. Melting curve analysis of an SNP with nearest neighbor symmetry after addition of suboptimal amounts of wild type DNA and PCR amplification.

Three samples of each genotype (WT = wild type, HET = heterozygous, MUT = homozygous mutant) were mixed with different amounts of wild type DNA to obtain different suboptimal reference DNA fractions. Wild type DNA fractions of 9/28, 1/2, and 19/28 are shown in Panels A, B, and C, respectively and can be compared to the predicted heteroduplex proportions of Fig. 3. Samples of the same genotype usually appear as single curves because of high-resolution analysis.

Figure 6. TGCE data of an SNP with nearest neighbor symmetry after addition of an optimal amount of wild type DNA and PCR amplification.

Three samples of each genotype (

……..

wild type,

______

heterozygous 187C>G, ------- homozygous 187C>G) were mixed with wild type DNA to obtain a reference DNA fraction of 1/7. After

amplification and separation by TGCE, data was normalized by shifting and scaling the largest peaks to a common location and magnitude. Mutant homozygous curves were approximately equidistant from the wild type curves and the barely altered heterozygous curves.

Figure S1. Theoretical melting curves of duplexes, their mixtures and differences.

((((Not edited, consider deleting)))) Theoretical melting curves from DNA which is heterozygous or consists of a mixture of two genotypes are a mathematical superposition of the theoretical melting curves of the individual duplexes formed by hybridization of two types of forward strands and two types of reverse strands in proportion to their relative concentrations. These curves were calculated using nearest-neighbor thermodynamic models and shown here along with their superposition. Homoduplexes with complementary C:G and G:C base pairs at the SNP locus have identical melting curves to the right. Heteroduplexes with mismatched base pairs at the SNP have distinct melting curves to the left (C:C left of G:G). The equally weighted average of all duplexes results in the theoretical heterozygous melting curve in the center. The difference of the theoretical wild type and heterozygous melting curves is also shown, along with the theoretical universal difference curve given by the homoduplex melting curve minus the mean heteroduplex melting curve. As the theory requires, the unmixed wild type minus heterozygous difference curve is 0.5 times the universal difference curve, the factor representing the heteroduplex content of the unmixed heterozygote.

Figure S1. The dependence of heteroduplex proportion on genotype and reference

DNA fraction.

The predicted heteroduplex proportion of homozygous mutant (m(x)) or heterozygous (h(x)) DNA when mixed with wild type DNA is shown. The magnitude of the difference in heteroduplex proportions between heterozygous and homozygous mutant samples is given by |h(x)-m(x)|. Since mixed wild type samples have no heteroduplex content, m(x) and h(x) also give the absolute heteroduplex proportion difference between mixtures of their respective genotypes and wild type. According to the theory, melting curve separation is proportional to heteroduplex content difference, so we wish to maximize the smallest of these differences, denoted by s(x), the lowest of the three graphs throughout the interval 0 to 1. The reference DNA fraction x which maximizes s(x) and therefore provides the greatest separation of heteroduplex content among genotypes also resolves their melting curves most effectively. According to the theory, this occurs at x =

1

7

, indicated by the sharp peak on the graph of s(x).

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