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<H1><A NAME="SECTION00010000000000000000">
1 Name </A>
</H1>
<SMALL>MELTING</SMALL> - nearest-neighbor computation of nucleic acid hybridation

<H1><A NAME="SECTION00020000000000000000">
2 Synopsis</A>
</H1>
<B>melting</B> [<I>options </I>]  

<H1><A NAME="SECTION00030000000000000000">
3 Description </A>
</H1>

<P>
<SMALL>MELTING</SMALL> computes, for a nucleic acid duplex, the enthalpy and the
entropy of the helix-coil transition, and then its melting temperature. Three
types of hybridisation are possible: DNA/DNA, DNA/RNA, and RNA/RNA. The program
uses the method of nearest-neighbors. The set of thermodynamic parameters can be
easely changed, for instance following an experimental breakthrough. Melting is
a free program in both sense of the term. It comes with no cost and it is
open-source. In addition it is coded in ISO C and can be compiled on any
operating system. Some perl scripts are provided to show how melting can be used
as a block to construct more ambitious programs.

<P>
If you use <SMALL>MELTING</SMALL>, please quote

<P>
<BLOCKQUOTE>
Le Nov&#232;re. <SMALL>MELTING</SMALL>, a free tool to compute the
    melting temperature of nucleic acid duplex. <I>Bioinformatics</I>, 17: 1226-1227. 

</BLOCKQUOTE>

<P>

<H1><A NAME="SECTION00040000000000000000">
4 Options </A>
</H1>

<P>
The options are treated sequentially. If there is a conflict between the value
of two options, the latter normally erases the former.

<P>
<DL>
<DT><STRONG><B>-A</B><I>file.nn</I></STRONG></DT>
<DD>
<BR>
Informs the program to use <I>file.nn</I> as an alternative set of
  nearest-neighbor parameters, rather than the default for the specified
  hybridisation type (option <B>-H</B>). The standard distribution of melting
  provides some files ready-to-use: <I>all97a.nn</I> (Allawi et al 1997),
  <I>bre86a.nn</I> (Breslauer et al 1986), <I>san96a.nn</I> (SantaLucia et
  al 1996), <I>sug96a.nn</I> (Sugimoto et al 1996), <I>san04a.nn</I> (Santalucia 
  et al 2004) (DNA/DNA),
  <I>fre86a.nn</I> (Freier et al 1986), <I>xia98a.nn</I> (Xia et al 1998)
  (RNA/RNA) and <I>sug95a.nn</I> (Sugimoto et al 1995) (DNA/RNA). The program
  will look for the file in a directory specified during the installation.
  However, if an environment variable NN_PATH is defined, melting will search
  in this one first. Be careful, the option <B>-A </B> changes the default
  parameter set defined by the option <B>-H.</B>
</DD>
<DT><STRONG><B>-C</B><I>complementary_sequence</I></STRONG></DT>
<DD>
<BR>
Enters the complementary sequence, from 3' to 5'. This option is mandatory if
  there are mismatches between the two strands. If it is not used, the program
  will compute it as the complement of the sequence entered with the option
  <B>-S</B>
</DD>
<DT><STRONG><B>-D</B><I>dnadnade.nn</I></STRONG></DT>
<DD>
<BR>
Informs the program to use the file <I>dnadnade.nn</I> to compute the
  contribution of dangling ends to the thermodynamic of helix-coil transition.
  The dangling ends are not taken into account by the approximative mode.
</DD>
<DT><STRONG><B>-F</B><I>factor</I>  </STRONG></DT>
<DD>
<BR>
This is the a correction factor used to modulate the effect of the nucleic
  acid concentration in the computation of the melting temperature. See section
  ALGORITHM for details.
</DD>
<DT><STRONG><B>-G</B><I>x.xxe-xx</I>  </STRONG></DT>
<DD>
<BR>
Magnesium  concentration  (No maximum concentration for the moment). The effect  
   of  ions  on  thermodynamic  stability  of nucleic  acid duplexes is complex,
   and the correcting functions are  at  best rough  approximations.The published 
   Tm  correction formula for divalent Mg<sup>2+</sup> ions of Owczarzy et al.(2008) can
   take in account the competitive binding of monovalent and divalent ions on DNA. 
   However this formula is only for DNA duplexes.
</DD>
<DT><STRONG><B>-h</B></STRONG></DT>
<DD>
<BR>
Displays a short help and quit with EXIT_SUCCESS. 
</DD>
<DT><STRONG><B>-H</B><I>hybridisation_type</I></STRONG></DT>
<DD>
<BR>
Specifies the hybridisation type. This will set the nearest-neighbor set to
  use if no alternative set is provided by the option <B>-A</B> (remember the
  options are read sequentially). Moreover this parameter determines the
  equation to use if the sequence length exceeds the limit of application of the
  nearest-neighbor approach (arbitrarily set up by the author). Possible values
  are <I>dnadna</I>, <I>dnarna</I> and <I>rnadna</I> (synonymous), and
  <I>rnarna</I>. For reasons of compatibility the values of the previous
  versions of melting <I>A,B,C,F,R,S,T,U,W</I> are still available although
  <B>strongly </B> deprecated. Use the option <B>-A</B> to require an
  alternative set of thermodynamic parameters. <B>Important:</B> If the duplex
  is a DNA/RNA heteroduplex, the sequence of the DNA strand has to be entered
  with the option <B>-S</B>
</DD>
<DT><STRONG><B>-I</B><I>input_file</I>  </STRONG></DT>
<DD>
<BR>
Provides the name of an input file containing the parameters of the
run. The input has to contain one parameter per line, formatted as in
the command line. The order  is not important, as well as blank lines.
example:   

<P>
<PRE>
 -Hdnadna  
 -Asug96a.nn
 -SAGCTCGACTC
 -CTCGAGGTGAG
 -N0.2
 -P0.0001 
 -v 
 -Ksan96a
</PRE>

<P>
</DD>
<DT><STRONG><B>-i</B><I>file.nn</I></STRONG></DT>
<DD>
<BR>
  Informs  the  program to use file.nn as an alternative set  of  inosine pair 
  parameters, rather than  the  default  for the specified hybridisation type. 
  The standard distribution of melting provides some  files ready-to-use:  san05a.nn 
 (Santalucia et al 2005) for deoxyinosine in DNA duplexes, bre07a.nn (Brent M Znosko 
  et al 2007)for inosine in RNA duplexes. Note  that  not all the inosine mismatched 
  wobble's pairs have been investigated. Therefore it could be impossible to  compute
  the Tm of a duplex with inosine pairs. Moreover, those inosine pairs are not taken 
  into account by the  approximative mode.
</DD>
<DT><STRONG><B>-K</B><I>salt_correction</I></STRONG></DT>
<DD>
<BR>
Permits to chose another correction for the concentration in sodium. Currently, 
one can chose between <I>wet91a, san96a, san98a</I>.  See section ALGORITHM 
</DD>
<DT><STRONG><B>-k</B><I>x.xxe-xx</I>  </STRONG></DT>
<DD>
<BR>
   Potassium  concentration  (No maximum concentration for the moment). The effect of ions 
   on  thermodynamic  stability  of nucleic  acid duplexes is complex, and the correcting 
   functions are  at  best rough  approximations.The published  Tm  correction formula for 
   sodium ions of Owczarzy et al.(2008) is therefore also applicable to buffers containing Tris or
   KCl. Monovalent K<sup>+</sup>, Na<sup>+</sup>, Tris<sup>+</sup> ions  stabilize  DNA duplexes 
   with similar potency, and their effects on duplex stability are additive. However this formula 
   is only for DNA duplexes.
</DD>
<DT><STRONG><B>-L</B></STRONG></DT>
<DD>
<BR>
Prints the legal informations and quit
  with EXIT_SUCCESS. 
</DD>
<DT><STRONG><B>-M</B><I>dnadnamm.nn</I></STRONG></DT>
<DD>
<BR>
Informs the program to use the file  <I>dnadnamm.nn</I> to compute
the contribution of mismatches to the thermodynamic of helix-coil
transition. Note that not all the mismatched Crick's pairs have been
investigated. Therefore it could be impossible to compute the Tm of a
mismatched duplex. Moreover, those mismatches are not taken into
account by the approximative mode. 
</DD>
<DT><STRONG><B>-N</B><I>x.xxe-xx</I>  </STRONG></DT>
<DD>
<BR>
Sodium concentration (between 0 and 10 M). The effect of ions on thermodynamic
  stability of nucleic acid duplexes is complex, and the correcting functions
  are at best rough approximations. Moreover, they are generally reliable only
  for [Na<sup>+</sup>] belonging to [0.1,1&nbsp;M]. If there are no other ions in 
  solution, we can use only the sodium correction. In the other case, we use the Owczarzy's 
  algorithm.
</DD>
<DT><STRONG><B>-O</B><I>output_file</I></STRONG></DT>
<DD>
<BR>
The output is directed to this file instead of the standard
output. The name of the file can be omitted. An automatic name is then
generated, of the form  meltingYYYYMMMDD_HHhMMm.out (of course, 
on POSIX compliant systems, you  can emulate this with the redirection 
of stdout to a file constructed with the program date).  
</DD>
<DT><STRONG><B>-P</B><I>x.xxe-xx</I></STRONG></DT>
<DD>
<BR>
Concentration of the nucleic acid strand in excess (between 0 and 0.1 M).
</DD>
<DT><STRONG><B>-p</B></STRONG></DT>
<DD>
<BR>
Return the directory supposed to contain the sets of calorimetric parameters and quit with
EXIT_SUCCESS. If the environment variable NN_PATH is set, it is returned. Otherwise, the value
defined by default during the compilation is returned.
</DD>
<DT><STRONG><B>-q</B>  </STRONG></DT>
<DD>
<BR>
Turn off the interactive correction of wrongly entered
parameter. Useful for run through a server, or a batch script. Default
is OFF (i.e. interactive on). The switch works in both sens. 
 Therefore if  <B>-q </B> has been set in an input file, another
 <B>-q </B> on the command line will switch the quiet mode OFF (same
 thing if two <B>-q </B> are set on the same command line).  
</DD>
<DT><STRONG><B>-S</B><I>sequence</I>  </STRONG></DT>
<DD>
<BR>
Sequence of one strand of the nucleic 
acid duplex, entered 5' to 3'. <B>Important:</B> If it is a DNA/RNA  heteroduplex, 
the sequence of the DNA strand has to be entered.  
Uridine and thymidine are 
considered as identical. The bases can be upper or lowercase.
</DD>
<DT><STRONG><B>-T</B><I>xxx</I>  </STRONG></DT>
<DD>
<BR>
Size threshold before approximative computation. The nearest-neighbour approach 
will be used only if the length of the sequence is inferior to this threshold.
</DD>
<DT><STRONG><B>-t</B><I>x.xxe-xx</I>  </STRONG></DT>
<DD>
<BR>
Tris buffer  concentration  (No maximum concentration for the moment). 
   The effect  of  ions  on  thermodynamic  stability  of nucleic  acid 
   duplexes is complex, and the correcting functions are  at  best
   rough  approximations.The published  Tm  correction formula for sodium ions of 
   Owczarzy et al (2008)is therefore also applicable to buffers containing Tris or
   KCl. Monovalent K<sup>+</sup>, Na<sup>+</sup>, Tris<sup>+</sup> ions  stabilize  DNA duplexes with similar potency, and 
   their effects on duplex stability are additive. However this formula is only for DNA 
   duplexes. Be aware, the Tris<sup>+</sup> ion concentration is about half of the total tris buffer
   concentration.
</DD>
<DT><STRONG><B>-v</B>  </STRONG></DT>
<DD>
<BR>
Control the verbose 
mode, issuing a lot more information about the current run  (try it once 
to see if you can get something interesting). Default is OFF. The  switch 
works in both sens. Therefore if  <B>-v </B> has been set in an input file, another 
<B>-v </B> on the command line will switch the verbose mode OFF (same thing if 
two  <B>-v </B> are set on the same command line).  
</DD>
<DT><STRONG><B>-V</B>  </STRONG></DT>
<DD>
<BR>
Displays the version number 
and quit with EXIT_SUCCESS 
</DD>
<DT><STRONG><B>-x</B>  </STRONG></DT>
<DD>
<BR>
Force the program to compute an approximative 
tm, based on G+C content. This option has to be used with caution. Note 
that such a calcul is increasingly incorrect when the length of  the duplex 
decreases. Moreover, it does not take into account nucleic acid concentration, 
which is a strong mistake.    

<P>
</DD>
</DL>

<P>

<H1><A NAME="SECTION00050000000000000000">
5 Algorithm </A>
</H1>

<P>

<H2><A NAME="SECTION00051000000000000000">
5.1 Thermodynamics of helix-coil transition of nucleic acid</A>
</H2>  
The nearest-neighbor approach is based on the fact that the helix-coil
transition works as a zipper. After an initial attachment, the hybridisation
propagates laterally.  Therefore, the process depends on the adjacent
nucleotides on each strand (the Crick's pairs).  Two duplexes with the same base
pairs could have different stabilities, and on the contrary, two duplexes with
different sequences but identical sets of Crick's pairs will have the same
thermodynamics properties (see Sugimoto et al. 1994).  This program first
computes the hybridisation enthalpy and entropy from the elementary parameters
of each Crick's pair.
<!-- MATH
 \begin{displaymath}
\begin{array}[t]{ccc}
  \Delta{}H&=&\delta{}h_\mathrm{initiation}+\sum \delta{}h_\mathrm{Crick's pair}\\
  \Delta{}S&=&\delta{}s_\mathrm{initiation}+\sum \delta{}s_\mathrm{Crick's pair}
  \end{array}
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 WIDTH="262" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="melting/img1.png"
 ALT="$\displaystyle \begin{array}[t]{ccc}
\Delta{}H&amp;=&amp;\delta{}h_\mathrm{initiation}+\...
...&amp;\delta{}s_\mathrm{initiation}+\sum \delta{}s_\mathrm{Crick's pair}
\end{array}$">
</DIV><P></P>

<P>
See Wetmur J.G. (1991) and SantaLucia (1998) 
for deep reviews on the nucleic  acid hybridisation and on the different 
set of nearest-neighbor parameters.    

<P>

<P></P>
<DIV ALIGN="CENTER"><A NAME="320"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1:</STRONG>
Comparison of experimental and computed Tm for various sets of
  nearest-neighbor parameters. [Na+]&nbsp;=&nbsp;1&nbsp;M, [nucleic acid]&nbsp;=&nbsp;4.10-4&nbsp;M</CAPTION>
<TR><TD><IMG
 SRC="melting/image1M.png" heigth="200"
 ></TD></TR>
</TABLE>
</DIV><P></P>

<P>

<P></P>
<DIV ALIGN="CENTER"><A NAME="321"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 2:</STRONG>
Comparison of experimental and computed Tm for various sets of
  nearest-neighbor parameters. [Na+]&nbsp;=&nbsp;0.11&nbsp;M, [nucleic acid]&nbsp;=&nbsp;8.10-6&nbsp;M</CAPTION>
<TR><TD><IMG
 SRC="melting/image0_11M.png" heigth="200"
></TD></TR>
</TABLE>
</DIV><P></P>

<P>

<H2><A NAME="SECTION00052000000000000000">
5.2 Effect of mismatches and dangling ends</A>
</H2>  

<P>
The mismatching (inosine  mismatches  included) pairs are also taken into account. However the thermodynamic
parameters are still not available for every possible cases (notably when both
positions are mismatched). In such a case, the program, unable to compute any
relevant result, will quit with a warning.  The two first and positions cannot
be mismatched. in such a case, the result is unpredictable, and all cases are
possible. for instance (see Allawi and SanLucia 1997), the duplex

<DIV ALIGN="LEFT">
<TT>
 A &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;T &nbsp;
<BR>&nbsp;<U>G</U>TGAGCTCA<U>T</U> &nbsp;
<BR>&nbsp;<U>T</U>ACTCGAGT<U>G</U> &nbsp;
<BR>
T &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A &nbsp;&nbsp;
<BR></TT>
</DIV>

<P>
is more stable than 

<P>

<DIV ALIGN="LEFT">
<TT>
 A<U>G</U>TGAGCTCA<U>T</U>T 
<BR>
T<U>T</U>ACTCGAGT<U>G</U>A 
<BR></TT>
</DIV>

<P>
The dangling ends, that is the unmatched terminal nucleotides, can be taken into
account.

<P>

<H2><A NAME="SECTION00053000000000000000">
5.3 Example</A>
</H2>

<P>
<P></P>
<DIV ALIGN="CENTER"><!-- MATH
 \begin{multline*}
\Delta H {\mbox{\texttt{AGCGATGAA-}} \choose \mbox{\texttt{-CGCTGCTTT}}} =
\Delta H {\mbox{\texttt{AG}} \choose \mbox{\texttt{-C}} } + 
\Delta H {\mbox{\texttt{A-}} \choose \mbox{\texttt{TT}} } \\+
\Delta H {\mbox{\texttt{G}} \choose \mbox{\texttt{C}} }_\mathrm{init} +
\Delta H {\mbox{\texttt{A}} \choose \mbox{\texttt{T}} }_\mathrm{init} \\+
\Delta H {\mbox{\texttt{GC}} \choose \mbox{\texttt{CG}} } +
\Delta H {\mbox{\texttt{CG}} \choose \mbox{\texttt{GC}} } +
2x \Delta H {\mbox{\texttt{GA}} \choose \mbox{\texttt{CT}} } +
\Delta H {\mbox{\texttt{AA}} \choose \mbox{\texttt{TT}} } \\+
\Delta H {\mbox{\texttt{A\underline{T}}} \choose \mbox{\texttt{T\underline{G}}} } +
\Delta H {\mbox{\texttt{\underline{T}G}} \choose \mbox{\texttt{\underline{G}C}} }
\end{multline*}
 -->
<IMG
 SRC="melting/img2.png"
 ALT="\begin{multline*}
\Delta H {\mbox{\texttt{AGCGATGAA-}} \choose \mbox{\texttt{-CG...
...texttt{\underline{T}G}} \choose \mbox{\texttt{\underline{G}C}} }
\end{multline*}"></DIV>
<BR CLEAR="ALL">
<P><P></P>

<P>
(The same computation is performed for <I>&Delta;G</I>)

<P>

<H2><A NAME="SECTION00054000000000000000">
5.4 The melting temperature </A>
</H2>  
Then the melting temperature is computed by the following formula:   

<P>
<TABLE CELLPADDING=3>
<TR><TD ALIGN="RIGHT">Tm</TD>
<TD ALIGN="CENTER">=</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=115><!-- MATH
 \begin{math}
\frac{\displaystyle \Delta{}H}{\displaystyle \Delta{}S + R \ln (C_T/F)} \hspace{2em} +
\end{math}
 -->
 <IMG
 SRC="melting/img4.png"
 ALT="$ \frac{\displaystyle \Delta{}H}{\displaystyle \Delta{}S + R \ln (C_T/F)} \hspace{2em} + $"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=158><!-- MATH
 \begin{math}
\mathcal{F}([\mathrm{Na}^+]) - 273.15
\end{math}
 -->
 <IMG
 SRC="melting/img5.png"
 ALT="$ \mathcal{F}([\mathrm{Na}^+]) - 273.15 $"></TD>
</TR>
<TR><TD ALIGN="RIGHT">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=115>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=158>&nbsp;</TD>
</TR>
<TR><TD ALIGN="RIGHT">&nbsp;</TD>
<TD ALIGN="CENTER">&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=115><FONT SIZE="-1"><I>Tm</I> in K (for [Na+] = 1&nbsp;M)    </FONT></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=158><FONT SIZE="-1"><I>correction</I> for the 
salt concentration (if there are only Na+ cations in the solution) and to get the temperature in degree Celsius. (In fact 
some corrections are directly included in the <I>&Delta;S</I>. See that of SanLucia 
1998)    
</FONT></TD>
</TR>
</TABLE>

<P>

<H2><A NAME="SECTION00055000000000000000">
5.5 Correction for the concentration of nucleic acid </A>
</H2>  

<P>
Many thanks to Ivano Zara (zarivan@cribi.unipd.it), who gave me most of
the following explanation.

<P>
In a reaction <!-- MATH
 $A + B \rightleftharpoons D$
 -->
<IMG
 ALIGN="center"
 SRC="melting/img6.png"
 ALT="$ A + B \rightleftharpoons D$">, where <I>A</I> is the strand in
excess, <I>B</I> the other strand, and <I>D</I> the duplex, and where the
oligonucleotides <I>are not self-complementary</I>, 
<!-- MATH
 \begin{displaymath}
\Delta G = \Delta G_0 - RT lnK = \Delta H_0 - T \Delta S_0 - RT lnK
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img7.png"
 ALT="$\displaystyle \Delta G = \Delta G_0 - RT lnK = \Delta H_0 - T \Delta S_0 - RT lnK
$">
</DIV><P></P>
and 
<!-- MATH
 \begin{displaymath}
K = \frac{[A][B]}{[D]}
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img8.png"
 ALT="$\displaystyle K = \frac{[A][B]}{[D]}
$">
</DIV><P></P>
If &xi; is the fraction of molecules <I>B</I> that forms the duplex,
<BR>
<DIV ALIGN="CENTER">
<!-- MATH
 \begin{eqnarray*}
\   [D] & = & \xi [B]_0 \\
\   \mbox{}[B] & = & [B]_0 - [D] = [B]_0 - \xi [B]_0 = [B]_0 ( 1 - \xi ) \\
  \mbox{}[A] & = & [A]_0 - [D] = [A]_0 - \xi [B]_0
\end{eqnarray*}
 -->
<TABLE CELLPADDING="0" ALIGN="CENTER" WIDTH="100%">
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
 SRC="melting/img10.png"
 ALT="$\displaystyle \ [D]$"></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
 SRC="melting/img11.png"
 ALT="$\displaystyle =$"></TD>
<TD ALIGN="LEFT" NOWRAP><IMG
 SRC="melting/img12.png"
 ALT="$\displaystyle \xi [B]_0$"></TD>
<TD WIDTH=10 ALIGN="RIGHT">
&nbsp;</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT"><IMG
 SRC="melting/img13.png"
 ALT="$\displaystyle \ $">&nbsp; &nbsp;&nbsp; <IMG
 SRC="melting/img14.png"
 ALT="$\displaystyle [B]$"></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
 SRC="melting/img11.png"
 ALT="$\displaystyle =$"></TD>
<TD ALIGN="LEFT" NOWRAP><IMG
 SRC="melting/img15.png"
 ALT="$\displaystyle [B]_0 - [D] = [B]_0 - \xi [B]_0 = [B]_0 ( 1 - \xi )$"></TD>
<TD WIDTH=10 ALIGN="RIGHT">
&nbsp;</TD></TR>
<TR VALIGN="MIDDLE"><TD NOWRAP ALIGN="RIGHT">&nbsp; <IMG
 SRC="melting/img16.png"
 ALT="$\displaystyle [A]$"></TD>
<TD WIDTH="10" ALIGN="CENTER" NOWRAP><IMG
 SRC="melting/img11.png"
 ALT="$\displaystyle =$"></TD>
<TD ALIGN="LEFT" NOWRAP><IMG
 SRC="melting/img17.png"
 ALT="$\displaystyle [A]_0 - [D] = [A]_0 - \xi [B]_0$"></TD>
<TD WIDTH=10 ALIGN="RIGHT">
&nbsp;</TD></TR>
</TABLE></DIV>
<BR CLEAR="ALL"><P></P>
Therefore,
<!-- MATH
 \begin{displaymath}
K = \frac{([A]_0 - \xi [B]_0) [B]_0 ( 1 - \xi )}{\xi [B]_0} = \frac{([A]_0 - \xi [B]_0) ( 1 - \xi )}{\xi}
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img18.png"
 ALT="$\displaystyle K = \frac{([A]_0 - \xi [B]_0) [B]_0 ( 1 - \xi )}{\xi [B]_0} = \frac{([A]_0 - \xi [B]_0) ( 1 - \xi )}{\xi}
$">
</DIV><P></P>
and, at melting temperature, when <IMG
 ALIGN="center"
 SRC="melting/img19.png"
 ALT="$ \xi = 1/2$">, 
<!-- MATH
 \begin{displaymath}
K = [A]_0 - \frac{1}{2} [B]_0
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img20.png"
 ALT="$\displaystyle K = [A]_0 - \frac{1}{2} [B]_0
$">
</DIV><P></P>
If both strands are present in equivalent amount, <!-- MATH
 $[A]_0 = [B]_0$
 -->
<IMG
ALIGN="center" 
SRC="melting/img21.png"
 ALT="$ [A]_0 = [B]_0$"> and
<!-- MATH
 $C_T = [A]_0 + [B]_0$
 -->
<IMG
ALIGN="center" 
 SRC="melting/img22.png"
 ALT="$ C_T = [A]_0 + [B]_0$">, then <!-- MATH
 $K = \frac{C_T}{4}$
 -->
<IMG
ALIGN="center" 
 SRC="melting/img23.png"
 ALT="$ K = \frac{C_T}{4}$"> (<IMG
 SRC="melting/img24.png"
 ALT="$ F=4$">). If <!-- MATH
 $[A]_0 \gg
[B]_0$
 -->
<IMG
ALIGN="center" 
 SRC="melting/img25.png"
 ALT="$ [A]_0 \gg
[B]_0$">, then <!-- MATH
 $C_T \approx [A]_0$
 -->
<IMG
ALIGN="center" 
 SRC="melting/img26.png"
 ALT="$ C_T \approx [A]_0$"> and <!-- MATH
 $K \approx [A]_0 \approx C_T$
 -->
<IMG
ALIGN="center" 
 SRC="melting/img27.png"
 ALT="$ K \approx [A]_0 \approx C_T$"> (<IMG
 SRC="melting/img28.png"
 ALT="$ F=1$">).
If the oligonucleotides are self-complementary, <!-- MATH
 $C_T = [A]_0$
 -->
<IMG
ALIGN="center" 
 SRC="melting/img29.png"
 ALT="$ C_T = [A]_0$"> and (<IMG
ALIGN="center" 
 SRC="melting/img28.png"
 ALT="$ F=1$">).

<P>
Note however that <SMALL>MELTING</SMALL> makes the assumption of no self-assembly,
<I>i.e.</I>  the computation does not take any entropic term to correct for
self-complementarity.

<P>

<H2><A NAME="SECTION00056000000000000000">
5.6 Correction for the concentration of salt </A>
</H2>  
If there are only sodium ions in the solution, we can use the following
corrections.  the correction can be chosen between <I>wet91a,</I> presented in
Wetmur 1991 <I>i.e.</I>
<!-- MATH
 \begin{displaymath}
\   16.6  \log \frac{[\mathrm{Na}^+]}{1 + 0.7 [\mathrm{Na}^+]} + 3.85
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img30.png"
 ALT="$\displaystyle \ 16.6 \log \frac{[\mathrm{Na}^+]}{1 + 0.7 [\mathrm{Na}^+]} + 3.85
$">
</DIV><P></P>

<P>
<I>san96a</I> presented in SantaLucia et al. 1996 
<I>i.e.</I>  
<!-- MATH
 \begin{displaymath}
12.5  \log [\mbox{Na}^+]
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 ALIGN="center"
 SRC="melting/img31.png"
 ALT="$\displaystyle 12.5 \log [$">Na<IMG
 ALIGN="center"
 SRC="melting/img32.png"
 ALT="$\displaystyle ^+]
$">
</DIV><P></P>
and  <I>san98a</I> presented in SantaLucia 1998 <I>i.e.</I> a correction 
of the entropic term without modification of enthalpy  
<!-- MATH
 \begin{displaymath}
\   \Delta{}S=\Delta{}S_{[\mathrm{Na}^+]=1\;\mathrm{M}}+0.368 (N-1) \ln [\mathrm{Na}^+]
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img33.png"
 ALT="$\displaystyle \ \Delta{}S=\Delta{}S_{[\mathrm{Na}^+]=1\;\mathrm{M}}+0.368 (N-1) \ln [\mathrm{Na}^+]
$">
</DIV><P></P>
Where <I>N</I> is the length of the duplex (SantaLucia 1998 actually used 'N' the number of non-terminal phosphates, that is effectively equal to our N-1).   

<P>

<P></P>
<DIV ALIGN="CENTER"><A NAME="259"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 3:</STRONG>
Comparison of experimental and computed Tm for various correction
of salt concentration.</CAPTION>
<TR><TD><IMG
 SRC="melting/salt.png"
 ALT="\includegraphics[]{salt.eps}"></TD></TR>
</TABLE>
</DIV><P></P>

<P>

<H2><A NAME="SECTION00057000000000000000">
5.7 Correction for the concentration of ions when other monovalent ions such as 
Tris<sup>+</sup> and K<sup>+</sup> or divalent Mg<sup>2+</sup> ions are added</A>
</H2>  

If there are only Na+ ions, we can use the correction for the concentration of salt
(see above). In the opposite case, we will use the magnesium and monovalent ions correction
from <I>Owczarzy et al (2008)</I>. (only for DNA duplexes)
       
       <P></P>
<DIV ALIGN="CENTER">
[Mon+] = [Na<sup>+</sup>] + [K<sup>+</sup>] + [Tris<sup>+</sup>]
</DIV><P></P>

Where [Tris<sup>+</sup>] is equal to half of total tris buffer concentration. <I>(in the option -t, it is the Tris buffer concentration
which is entered)</I>. <P></P>
       
When the divalent ions are the only ions present, the melting temperature is :

<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/magnesium1.png" height="300" >
</DIV>
<P></P>    
       where : 
       <P></P>a = 3.92 x 10<sup>-5</sup>
       <P></P>b = 9.11 x 10<sup>-6</sup>
       <P></P>c = 6.26 x 10<sup>-5</sup>
       <P></P>d = 1.42 x 10<sup>-5</sup>
       <P></P>e = 4.82 x 10<sup>-4</sup>
       <P></P>f = 5.25 x 10<sup>-4</sup>
       <P></P>g = 8.31 x 10<sup>-5</sup>.
       <P></P>
       Fgc is the fraction of GC base pairs in the sequence and 
       Nbp is the length of the sequence (Number of base pairs).
       <P></P>
       
       When there are both monovalent and divalent ions, there are several cases because we can have
       a competitive DNA binding between monovalent and divalent 
       cations  :
       <P></P>
       
       If the following ratio :<P></P>
   <DIV ALIGN="CENTER">       <IMG
 SRC="melting/ratio.png" height="60" >
</DIV> <P></P>  
is inferior to 0.22, monovalent ion influence is dominant, divalent cations can be 
disregarded and the melting temperature is :
       
 <P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/magnesium2.png" height="200">
</DIV> <P></P>

<P></P>
<DIV ALIGN="CENTER"><A NAME="320"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 4:</STRONG>
Comparison of experimental and computed Tm with the algorithm published in Owczarzy et al.(2008). [Mon+]&nbsp;=&nbsp;0.055&nbsp;M,[Mg2+]&nbsp;=&nbsp;0&nbsp;M, [nucleic acid]&nbsp;=&nbsp;2.10-6&nbsp;M</CAPTION>
<TR><TD><IMG
 SRC="melting/Owczarzy2.png" heigth="350"
 ></TD></TR>
</TABLE><P></P></DIV>
        
       If the ratio is included in [0.22, 6[,
       we must take in account both Mg<sup>2+</sup> and monovalent cations 
       concentrations. The melting temperature is calculated with the first equation but with monovalent ions concentration dependent parameters a, d and g :
	<DIV ALIGN="CENTER">
 
	<P></P>
	a = 3.92 x 10<sup>-5</sup> x (0.843 - 0.352 x [Mon<sup>+</sup>]0.5 x ln([Mon<sup>+</sup>])) 
       <P></P>
       d = 1.42 x 10<sup>-5</sup> x (1.279 - 4.03 x 10<sup>-3</sup> x ln([mon<sup>+</sup>]) - 8.03 x 10<sup>-3</sup> x ln([mon<sup>+</sup>] x ln([mon<sup>+</sup>])
       <P></P> 
       g = 8.31 x 10<sup>-5</sup> x (0.486 - 0.258 x ln([mon<sup>+</sup>]) + 5.25 x 10<sup>+</sup> x ln([mon<sup>+</sup>] x ln([mon<sup>+</sup>] x ln([mon<sup>+</sup>])
       <P></P>.
       
       and b, c, e, f are constant.
       </DIV>
       
       <P></P>
<DIV ALIGN="CENTER"><A NAME="320"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 5:</STRONG>
Comparison of experimental and computed Tm with the algorithm published in Owczarzy et al.(2008). [Mon+]&nbsp;=&nbsp;0.055&nbsp;M,[Mg2+]&nbsp;=&nbsp;0.0015&nbsp;M, [nucleic acid]&nbsp;=&nbsp;2.10-6&nbsp;M</CAPTION>
<TR><TD><IMG
 SRC="melting/Owczarzy3.png" heigth="350"
 ></TD></TR>
</TABLE><P></P></DIV>
       
       Finally, if the ratio is superior to 6,
       divalent ion influence is dominant, monovalent cations can be disregarded and the melting temperature is calculated with the first equation and the constant parameters a, b, c, d,
       e, f, g.<P></P>

<DIV ALIGN="CENTER"><A NAME="320"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6:</STRONG>
Comparison of experimental and computed Tm with the algorithm published in Owczarzy et al.(2008). [Mon+]&nbsp;=&nbsp;0.001&nbsp;M,[Mg2+]&nbsp;=&nbsp;0.0015&nbsp;M, [nucleic acid]&nbsp;=&nbsp;2.10-6&nbsp;M</CAPTION>
<TR><TD><IMG
 SRC="melting/Owczarzy1.png" heigth="350"
 ></TD></TR>
</TABLE><P></P></DIV>

<H2><A NAME="SECTION00058000000000000000">
5.8 Long sequences </A>
</H2>  
 It is important to realise that the nearest-neighbor approach 
has been established  on small oligonucleotides. Therefore the use of <SMALL>MELTING</SMALL> 
in the non-approximative  mode is really accurate only for relatively short 
sequences (Although if the sequences are two short, let's say &lt; 6&nbsp;bp, the 
influence of extremities becomes too important and the  reliability decreases 
a lot). For long sequences an approximative mode has been designed. This mode is 
launched if the sequence length is higher than the value 
given by the option -T (the default threshold is 60 bp).

<P>
The melting temperature is computed by the following formulas:   

<P>
<SMALL>ADN/ADN</SMALL>:
<!-- MATH
 \begin{displaymath}
Tm = 81.5 + 16.6\log\frac{[\mathrm{Na}^+]}{1+0.7[\mathrm{Na}^+]} + 0.41\% GC - \frac{500}{size}
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img34.png"
 ALT="Tm = 81.5 + 16.6\log\frac{[\mathrm{Na}^+]}{1+0.7[\mathrm{Na}^+]} + 0.41\% GC - \frac{500}{size}">
</DIV><P></P>
<SMALL>ADN/ARN</SMALL>:
<!-- MATH
 \begin{displaymath}
Tm = 67 + 16.6\log\frac{[\mathrm{Na}^+]}{1+0.7[\mathrm{Na}^+]} + 0.8\% GC - \frac{500}{size}
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img35.png"
 ALT="Tm = 67 + 16.6\log\frac{[\mathrm{Na}^+]}{1+0.7[\mathrm{Na}^+]} + 0.8\% GC - \frac{500}{size}">
</DIV><P></P>
<SMALL>ARN/ARN</SMALL>:
<!-- MATH
 \begin{displaymath}
Tm = 78 + 16.6\log\frac{[\mathrm{Na}^+]}{1+0.7[\mathrm{Na}^+]} + 0.7\% GC - \frac{500}{size}
\end{displaymath}
 -->
<P></P>
<DIV ALIGN="CENTER">
<IMG
 SRC="melting/img36.png"
 ALT="Tm = 78 + 16.6\log\frac{[\mathrm{Na}^+]}{1+0.7[\mathrm{Na}^+]} + 0.7\% GC - \frac{500}{size}">

</DIV><P></P>

<P>
The usage of this mode is nevertheless  <B>strongly disencouraged.</B>   

<P>

<H2><A NAME="SECTION00059000000000000000">
5.9 Miscellaneous comments </A>
</H2>  
<SMALL>MELTING</SMALL> is currently accurate only when the hybridisation is performed
at pH 71.  The computation is valid only for the hybridisations performed
in aqueous medium. Therefore the use of denaturing agents such as formamide
completely invalidates the results.

<P>

<H1><A NAME="SECTION00060000000000000000">
6 References </A>
</H1>
Allawi 
H.T., SantaLucia J. (1997). Thermodynamics and NMR of internal G-T mismatches 
in DNA. <I>Biochemistry</I>  36: 10581-10594  
 
<P>
Allawi H.T., SantaLucia J. (1998). 
Nearest Neighbor thermodynamics parameters for internal G.A mismatches in DNA. 
<I> Biochemistry </I>
37: 2170-2179

<P>
Allawi H.T., SantaLucia J. (1998). 
Thermodynamics of internal C.T mismatches in DNA.
<I> Nucleic Acids Res </I>
26: 2694-2701

<P>
Allawi H.T., SantaLucia J. (1998). 
Nearest Neighbor thermodynamics of internal A.C mismatches in DNA: sequence 
dependence and pH effects.
<I> Biochemistry </I>
37: 9435-9444.

<P>
Bommarito S., Peyret N., SantaLucia J. (2000).  Thermodynamic parameters for DNA
sequences with dangling ends.  <I>Nucleic Acids Res</I> 28: 1929-1934

<P>
Breslauer K.J., Frank R., Bl&#246;cker 
H., Marky L.A. (1986). Predicting DNA duplex stability from the base sequence. 
 <I>Proc Natl Acad Sci USA</I>  83: 3746-3750   

<P>
Freier S.M., Kierzek R., Jaeger 
J.A., Sugimoto N., Caruthers M.H., Neilson T., Turner D.H. (1986). <I>Biochemistry</I> 
 83:9373-9377   
 
 <P> 
 Owczarzy R., Moreira B.G., You Y., Behlke M.B., Walder J.A.(2008) Predicting stability of DNA duplexes 
 in solutions containing Magnesium and Monovalent Cations. <I>Biochemistry</I> 47: 5336-5353.  

<P> 
Peyret N., Seneviratne P.A., Allawi H.T., SantaLucia J. (1999). 
Nearest Neighbor thermodynamics and NMR of DNA sequences with internal 
A.A, C.C, G.G and T.T mismatches. 
dependence and pH effects.
<I> Biochemistry </I>
38: 3468-3477

<P>
SantaLucia J. Jr, Allawi H.T., Seneviratne P.A. (1996). Improved 
nearest-neighbor parameters for predicting DNA duplex stability. <I>Biochemistry</I> 
35: 3555-3562   

<P>
Sugimoto N., Katoh M., Nakano S., Ohmichi T., Sasaki M. (1994). 
RNA/DNA hybrid duplexes with identical nearest-neighbor base-pairs hve identical 
stability. <I>FEBS Letters</I> 354: 74-78   

<P>
Sugimoto N., Nakano S., Katoh M., Matsumura 
A., Nakamuta H., Ohmichi T., Yoneyama M., Sasaki M. (1995). Thermodynamic parameters 
to predict stability of RNA/DNA hybrid duplexes. <I>Biochemistry</I> 34: 11211-11216 

<P>
Sugimoto N., Nakano S., Yoneyama M., Honda K. (1996).  Improved thermodynamic 
parameters and helix initiation factor to predict stability of DNA duplexes. 
<I>Nuc Acids Res</I>  24: 4501-4505   

<P>
Watkins N.E., Santalucia J. Jr. (2005). Nearest-neighbor thermodynamics of deoxyinosine 
pairs in DNA duplexes. <I>Nucleic Acids Research</I> 33: 6258-6267

<P>
Wright D.J., Rice J.L., Yanker D.M., Znosko B.M. (2007). Nearest neighbor parameters for 
inosine-uridine pairs in RNA duplexes. <I>Biochemistry</I> 46: 4625-4634 

<P>
Xia T., SantaLucia J., Burkard M.E., Kierzek 
R., Schroeder S.J., Jiao X., Cox C., Turner D.H. (1998). Thermodynamics parameters 
for an expanded nearest-neighbor model for formation of RNA duplexes with 
Watson-Crick base pairs. <I>Biochemistry</I>  37: 14719-14735   

<P>
For review see: 

<P>
SantaLucia J. (1998) A unified view of polymer, dumbbell, and oligonucleotide 
DNA nearest-neighbor thermodynamics. <I>Proc Natl Acad Sci USA</I>  95: 1460-1465

<P>
SantaLucia  J., Hicks Donald (2004) The Thermodynamics of DNA structural motifs. 
<I>Annu. Rev. Biophys. Struct.</I> 33: 415-440 

<P>
Wetmur J.G. (1991) DNA probes: applications of the principles of nucleic 
acid hybridization. <I>Crit Rev Biochem Mol Biol</I> 26: 227-259   

<P>

<H1><A NAME="SECTION00070000000000000000">
7 Files </A>
</H1>
<DL COMPACT>
<DT><I>*.nn</I></DT>
<DD>Files containing the nearest-neighbor parameters, enthalpy and entropy, 
for each Crick's pair.  They have to be placed in a directory defined during 
the compilation or targeted by the  environment variable NN_PATH.  
</DD>
<DT><I>tkmelting.pl</I></DT>
<DD>A Graphical User Interface written in perl/tk is available for users
who prefer  the 'button and menu' approach.  
</DD>
<DT><I>*.pl</I></DT>
<DD>Scripts are available to 
use <SMALL>MELTING</SMALL> iteratively. For instance, the script multi.pl permits to predict 
the Tm of several duplexes in one shot. The script profil.pl allow
an interactive computation along a sequence, by sliding a window of specified width. 

<P>
</DD>
</DL>

<P>

<H1><A NAME="SECTION00080000000000000000">
8 See Also </A>
</H1>
New versions and 
related material can be found at <TT><A NAME="tex2html4"
  HREF="http://www.ebi.ac.uk/~lenov/meltinghome.html">http://www.ebi.ac.uk/~lenov/meltinghome.html</A></TT> 
  and at <TT><A HREF= "https://sourceforge.net/projects/melting/">https://sourceforge.net/projects/melting/</A></TT>

<P>
You can use <SMALL>MELTING</SMALL> through a web server at <TT><A NAME="tex2html5"
  HREF="http://bioweb.pasteur.fr/seqana
l/interfaces/melting.html">http://bioweb.pasteur.fr/seqana
l/interfaces/melting.html</A></TT>
<P>

<H1><A NAME="SECTION00090000000000000000">
9 Known Bugs </A>
</H1>
The infiles have to be ended by a blank line because otherwise the last line is not decoded.

<P>
If an infile is called, containing the 
address of another input file, it does not care of this latter.  If it 
is its own address, the program quit (is it a bug or a feature?).   

<P>
In interactive mode, a sequence can be entered on several lines with a backslash
<BR><TT>AGCGACGAGCTAGCCTA&#92;
<BR>
AGGACCTATACGAC</TT>
<BR>
If by mistake it is entered as  
<BR><TT>AGCGACGAGCTAGCCTA&#92;AGGACCTATACGAC</TT>

<P>
The backslash will be considered 
 as an illegal character. Here again, I do not think it is actually a bug 
(even if it is unlikely, there is a small probability that the  backslash 
could actually be a mistyped base).   

<P>

<H1><A NAME="SECTION000100000000000000000">
10 Copyright </A>
</H1>
Melting is copyright 
&#169;1997, 2009 by Nicolas Le Nov&#232;re and Marine Dumousseau   

<P>
This program is free software; 
you can redistribute it and/or modify it under the terms of the GNU General 
Public License as published by the Free Software Foundation; either version 
2 of the License, or (at your option) any later version.   
  This program 
is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; 
without even the implied warranty of MERCHANTABILITY or FITNESS FOR A 
PARTICULAR PURPOSE.  See the GNU General Public License for more details. 

<P>
You should have received a copy of the GNU General Public License 
along with this program; if not, write to the Free Software Foundation, 
Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA   

<P>

<H1><A NAME="SECTION000110000000000000000">
11 Acknowledgements</A>
</H1>
Nicolas Joly is an efficient and kind debugger and advisor.  Catherine
Letondal wrote the HTML interface to melting. Thanks to Nirav Merchant,
Taejoon Kwon, Leo Schalkwyk, Mauro Petrillo, Andrew Thompson, Wong Chee Hong, Ivano
Zara for their bug fixes and comments.  Thanks to Richard Owczarzy for his
magnesium correction. Thanks to Charles Plessy for the graphical interface files..
Finally thanks to the usenet helpers, particularly Olivier Dehon and Nicolas Chuche.


<P>

<H1><A NAME="SECTION000120000000000000000">
12 Authors </A>
</H1>
Nicolas Le Nov&#232;re and Marine Dumousseau, 
<BR>
EMBL-EBI, 
<BR>
Wellcome-Trust Genome Campus
<BR>
Hinxton Cambridge, CB10 1SD, UK
<BR>
lenov@ebi.ac.uk
<BR>


<P>

<H1><A NAME="SECTION000130000000000000000">
13 History </A>
</H1>
<P>
See the file ChangeLog for the changes of the versions 4 and more recent.

</BODY>
</HTML>