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\begin{center}

Notation: \\
Genotypes: \\
W = Wild-type, M = Mutant Homozygote, H = Mutant Heterozygote \\
\vspace{8ex}
Strands: \\
w = wild-type forward, $\bar{w}$ = wild-type reverse\\
m = mutant homozygote forward, $\bar{m}$ = mutant homozygote reverse\\

\vspace{8ex}

Table 1a. Wild-type and mutant homoduplex concentration fractions$\ ^1$ \\
Before dissociation:\\

\vspace{8ex}

\begin{tabular}{|c|c|c|c|c|c|c|}
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\hline
Genotype & [$w\bar{w}$] & [$m\bar{m}$] \\
W        &      $1$     &    $0$   \\
\hline

M        &      $x$      &   $1-x$  \\
\hline

H        &$x+{1-x\over2}={1+x \over 2}$& ${1-x \over 2}$ \\
\hline

\hline
\end{tabular}


\vspace{8ex}

Table 1b. Duplex concentration fractions$\ ^2$ \\
After dissociation and independent annealing:\\

\vspace{8ex}


\begin{tabular}{|c|c|c|c|c|c|c|}

\hline
Genotype & $[d_1]=[w\bar{w}]$  & $[d_2]= [w\bar{m}]$ & $[d_3]=[m\bar{w}]$ & $[d_4]=[m\bar{m}]$ \\
\hline

W      &  $1$      &    $0$      &     $0$      &    $0$   \\

\hline
M      &     $x^2$    &   $x(1-x)$   &   $x(1-x)$   &    $(1-x)^2$ \\

\hline
H &${(1+x)^2 \over 4}$ & ${1-x^2 \over 4}$ &${1-x^2 \over 4}$ &${(1-x)^2 \over 4}$ \\
\hline

\end{tabular}

\end{center}
$\ ^1$ The fractions are given relative to total concentration 1, 
when a fraction $x$ of wild-type DNA is mixed with fraction $1-x$ of the 
given genotype.  \\

$\ ^2$ The fractions are given relative to total concentration 1, and
are obtained as the products of strand fractions in Table 1b.


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Table 1c. Melting curves \\
The sum of duplex fractions from 1c times duplex melting curves\\

\vspace{8ex}

\begin{tabular}{|c|c|c|c|c|c|c|}

\hline
Genotype & Melting Curve \\
W      & $1F_1(T)$    \\
\hline
M      & $x^2 F_1(T) + x(1-x) F_2(T)   + x(1-x) F_3(T) + (1-x)^2 F_4(T)$ \\
\hline
H &
${(1+x)^2\over 4}F_1(T)+{1-x^2\over 4}F_2(T)+{1-x^2\over 4}F_3(T)+{(1-x)^2\over 4}F_4(T)$
\\
\hline
\end{tabular}


\vspace{8ex}

Table 1d. Melting curve differences\\

\vspace{8ex}

\begin{tabular}{|c|c|c|c|c|c|c|}

\hline
Genotype & Difference Curve \\
W-M      & $1- x^2 F_1(T) - x(1-x) F_2(T)   - x(1-x) F_3(T) - (1-x)^2 F_4(T)$ 
\\
\hline
W- H &
$1-{(1+x)^2\over 4}F_1(T)-{1-x^2\over 4}F_2(T)-{1-x^2\over 4}F_3(T)-{(1-x)^2\over 4}F_4(T)$
\\
\hline
\end{tabular}

\vspace{8ex}

Table 1e. Difference Curves When $F_1(T)=F_4(T)$ \\ 

\vspace{8ex}

\begin{tabular}{|c|c|c|}

\hline
Genotype & Difference Curve When $F_1(T)=F_4(T)$ \\ 
$W_=-M_=$ & $2x(1-x)[{F_1(T)+ F_4(T) \over 2} - {F_2(T)+ F_3(T) \over 2} ]=m(x)F(T)$ \\
\hline
$W_=- H_=$ & ${1-x^2 \over 2} [{F_1(T)+ F_4(T) \over 2} - {F_2(T)+ F_3(T) \over 2} ]=h(x)F(T)$ \\
\hline
$H_=- M_= $ & ${3x^2-4x +1 \over 2} [{F_1(T)+ F_4(T) \over 2} - {F_2(T)+ F_3(T) \over 2} ]=(h(x)-m(x))F(T)$ \\
\hline
\end{tabular}



\vspace{8ex}

Table 1f. Ordering of Absolute Heteroduplex Content Differences \\ 

\vspace{8ex}

\begin{tabular}{|c|c|c|c|c|c|c|}

\hline
Interval & Smallest, $s(x)$ & Middle & Largest \\
\hline
$0<x<{1 \over 7}$      & $m(x)$ & $ h(x)-m(x) $ & $h(x)$ \\
\hline
${1 \over 7} <x<{1 \over 3}$  & $ h(x)-m(x) $ & $m(x)$ & $h(x)$ \\
\hline
${1 \over 3} <x<1 $  & $ m(x)-h(x) $ & $h(x)$ & $m(x)$ \\
\hline
\end{tabular}


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1.~~ & 15 & \\
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1.~~ & 15 & \\
