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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"><!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998)originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan* with significant contributions from: Jens Lippmann, Marek Rouchal, Martin Wilck and others --><HTML><HEAD><TITLE>The energy dot plot</TITLE><META NAME="description" CONTENT="The energy dot plot"><META NAME="keywords" CONTENT="FEBS98-html"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"><LINK REL="STYLESHEET" HREF="FEBS98-html.css"><LINK REL="next" HREF="node11.html"><LINK REL="previous" HREF="node9.html"><LINK REL="up" HREF="node9.html"><LINK REL="next" HREF="node11.html"></HEAD><BODY BGCOLOR=#FFDEAD TEXT=#202020 LINK=#800000 ALINK=#ffff00 VLINK=#353976><!--Navigation Panel--><A NAME="tex2html175" HREF="node11.html"><IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="img/next_motif.gif"></A> <A NAME="tex2html172" HREF="node9.html"><IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="img/up_motif.gif"></A> <A NAME="tex2html166" HREF="node9.html"><IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="img/previous_motif.gif"></A> <A NAME="tex2html174" HREF="node1.html"><IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="img/contents_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html176" HREF="node11.html">Optimal and suboptimal foldings</A><B> Up:</B> <A NAME="tex2html173" HREF="node9.html">OUTPUT</A><B> Previous:</B> <A NAME="tex2html167" HREF="node9.html">OUTPUT</A><BR><BR><!--End of Navigation Panel--><H3><A NAME="SECTION00072100000000000000"><I>The energy dot plot</I></A></H3><P>A nucleic acid secondary structure dot plot is a triangular plot thatdepicts base pairs as dots or other symbols. We shall refer to thesesymbols as dots. A dot in column <I>i</I> and row <I>j</I> of a triangulararray, <!-- MATH: $\{ (i,j) | 1 \leq i \leq j \leq n \}$ --><IMG WIDTH="150" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img100.gif" ALT="$\{ (i,j) \vert 1 \leq i \leq j \leq n \}$">represents the base pair<I>i</I>.<I>j</I>. The advantage of a dot plot is that it can display the basepairs in more than 1 folding simultaneously. It can be used to comparea few foldings, or the base pair distribution in many millions offoldings. <P><I>Mfold</I> computes a number, <!-- MATH: $\Delta G(i,j)$ --><IMG WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img101.gif" ALT="$\Delta G(i,j)$">for every possible basepair, <I>i</I>.<I>j</I>. This is the minimum free energy of any folding thatcontains the <I>i</I>.<I>j</I> base pair. As above, we let <IMG WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img6.gif" ALT="$\Delta G$">be theoverall minimum folding free energy, and <!-- MATH: $\Delta \Delta G$ --><IMG WIDTH="42" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img9.gif" ALT="$\Delta \Delta G$">a userselected free energy increment. Clearly<BR><P></P><DIV ALIGN="CENTER"><!-- MATH: \begin{displaymath}\Delta G= \min_{1 \leq i < j \leq n} \Delta G(i,j).\end{displaymath} --><IMG WIDTH="166" HEIGHT="38" SRC="img102.gif" ALT="\begin{displaymath}\Delta G= \min_{1 \leq i < j \leq n} \Delta G(i,j).\end{displaymath}"></DIV><BR CLEAR="ALL"><P></P>The energy increment is derived from <IMG WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img6.gif" ALT="$\Delta G$">and <I>P</I>. That is,<!-- MATH: $\Delta \Delta G= P \times \Delta G/ 100$ --><IMG WIDTH="153" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img103.gif" ALT="$\Delta \Delta G= P \times \Delta G/ 100$">.The current convention isto lower <!-- MATH: $\Delta \Delta G$ --><IMG WIDTH="42" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img9.gif" ALT="$\Delta \Delta G$">to 12 kcal/mole when it would otherwisebe greater, and to raise it to 1 kcal/mole when it would otherwisebe smaller. Then the <I>energy dot plot</I> is defined to be thecollection of all base pairs <I>i</I>.<I>j</I> satisfying:<BR><P></P><DIV ALIGN="CENTER"><!-- MATH: \begin{displaymath}\Delta G(i,j) \leq \Delta G+ \Delta \Delta G.\end{displaymath} --><IMG WIDTH="167" HEIGHT="28" SRC="img104.gif" ALT="\begin{displaymath}\Delta G(i,j) \leq \Delta G+ \Delta \Delta G.\end{displaymath}"></DIV><BR CLEAR="ALL"><P></P>This dot plot contains the <B>superposition of all possiblefoldings</B> whose folding energy is within <!-- MATH: $\Delta \Delta G$ --><IMG WIDTH="42" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img9.gif" ALT="$\Delta \Delta G$">of theminimum folding energy. Typically, <!-- MATH: $|\Delta \Delta G|$ --><IMG WIDTH="51" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img105.gif" ALT="$\vert\Delta \Delta G\vert$">is smallcompared to <!-- MATH: $|\Delta G|$ --><IMG WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img106.gif" ALT="$\vert\Delta G\vert$">,or <I>P</I> is a small percentage. In this case,the <I>energy dot plot</I> contains the superposition of all close to optimalfoldings. <P>The <I>energy dot plot</I> gives an overall visual impression of how ``well-defined''the folding is. A cluttered plot, or cluttered regions, indicate eitherstructural plasticity (the lack of well-defined structure) or else theinability of the algorithm to predict a structure with confidence. Acouple of crude measures of ``well-definedness'' have been introducedin <I>mfold</I> . The first is ``P-num''. <!-- MATH: $P\!-\!num(i)$ --><IMG WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img107.gif" ALT="$P\!-\!num(i)$">is a measure of thelevel of promiscuity of <I>r</I><SUB><I>i</I></SUB> in its pairing with other bases infoldings within <!-- MATH: $\Delta \Delta G$ --><IMG WIDTH="42" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img9.gif" ALT="$\Delta \Delta G$">of <IMG WIDTH="29" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img6.gif" ALT="$\Delta G$">.It is the number of different basepairs, <I>i</I>.<I>j</I>, or <I>k</I>.<I>i</I> that can form in this set of foldings, and issimply the number of dots in the <I>i</I><SUP><I>th</I></SUP> row and <I>i</I><SUP><I>th</I></SUP> column ofthe <I>energy dot plot</I> . If <!-- MATH: $\delta(expression)$ --><IMG WIDTH="101" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img108.gif" ALT="$\delta(expression)$">is defined to be 1 when``expression'' is true, and 0 otherwise, then P-num may be defined as:<BR><P></P><DIV ALIGN="CENTER"><!-- MATH: \begin{displaymath}P\!-\!num(i) = \sum_{k < i} \delta (\Delta G(k,i) \leq \Delta G+ \Delta \Delta G) +\sum_{i < j} \delta (\Delta G(i,j) \leq \Delta G+ \Delta \Delta G).\end{displaymath} --><IMG WIDTH="541" HEIGHT="47" SRC="img109.gif" ALT="\begin{displaymath}P\!-\!num(i) = \sum_{k < i} \delta (\Delta G(k,i) \leq \Delta......{i < j} \delta (\Delta G(i,j) \leq \Delta G+ \Delta \Delta G).\end{displaymath}"></DIV><BR CLEAR="ALL"><P></P>P-num pertains to individual bases. H-num is ``well-definedness'' measure fora base pair <I>i</I>.<I>j</I>. It is the average value of the two P-num quantities,adjusted by removing the ``desirable'' <I>i</I>.<I>j</I> base pair. That is:<BR><P></P><DIV ALIGN="CENTER"><!-- MATH: \begin{displaymath}H\!-\!num(i,j) = ( P\!-\!num(i) + P\!-\!num(j) - 1 )/2.\end{displaymath} --><IMG WIDTH="351" HEIGHT="28" SRC="img110.gif" ALT="\begin{displaymath}H\!-\!num(i,j) = ( P\!-\!num(i) + P\!-\!num(j) - 1 )/2.\end{displaymath}"></DIV><BR CLEAR="ALL"><P></P>A helix, already defined as a collection of two or more consecutivebase pairs, may be described as a triple <I>i</I>,<I>j</I>,<I>k</I>, where <I>k</I> is thenumber of base pairs, and the actual base pairs are <!-- MATH: $i.j,i\!+\!1.j\!-\!1, \dots, i\!+\!k\!-\!1.j\!-\!k\!+\!1$ --><IMG WIDTH="231" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img111.gif" ALT="$i.j,i\!+\!1.j\!-\!1, \dots, i\!+\!k\!-\!1.j\!-\!k\!+\!1$">.When <I>k</I>=1, thehelix becomes a single base pair. With some abuse of notation, we mayalso write <!-- MATH: $H\!-\!num(i,j,k)$ --><IMG WIDTH="112" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img112.gif" ALT="$H\!-\!num(i,j,k)$">to be the H-num value of the helix,<I>i</I>,<I>j</I>,<I>k</I>. This is the average value of H-num over all the base pairs inthe helix.<P>There are 5 files associated with the <I>energy dot plot</I> . <P> `<SMALL>FILE_NAME.PLOT' : </SMALL> This is a text file that contains all thebase pairs on the <I>energy dot plot</I> , organized into helices for which <!-- MATH: $\Delta G(i,j)$ --><IMG WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img101.gif" ALT="$\Delta G(i,j)$">isconstant. The first record is a header, and each subsequent recorddescribes a single helix. The records are usually sorted by<!-- MATH: $\Delta G(i,j)$ --><IMG WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img101.gif" ALT="$\Delta G(i,j)$">,and are often filtered so that short helices or isolatedbase pairs (helices of length 1) in suboptimal foldings areremoved. Figure <A HREF="node10.html#PLOT">9</A> shows a sample plot file.<BR><DIV ALIGN="CENTER"><A NAME="PLOT"> </A><A NAME="829"> </A><TABLE WIDTH="70%" BORDER=5 CELLPADDING=10><CAPTION><STRONG>Figure 9:</STRONG>Selected records from a plot file. ``level''refers to a free energy range that is to be plotted in the same color,where 1 is always optimal. The ``level'' parameter is obsolete inthe newer plotting programs of <I> mfold</I> 3.0. ``istart'', ``jstart'' and``length'' define a helix and refer to <I>i</I>,<I>j</I>,<I>k</I>, respectively. The``energy'' is free energy expressed as an integer in 10<SUP><I>th</I></SUP>s of akcal/mole. Note that this is not the free energy of the helix, but themimimum free energy of any folding that contains the helix.</CAPTION><TR><TD BGCOLOR=#FFFFFF ALIGN=CENTER><PRE> level length istart jstart energy 1 8 206 242 -972 1 7 319 434 -972 1 7 108 141 -972 1 7 53 185 -972 1 6 334 412 -972 1 6 308 444 -972 1 6 288 472 -972 1 6 247 279 -972 ... 2 4 8 23 -971 2 2 69 78 -971 2 4 1 24 -970 2 2 10 17 -970 2 3 345 400 -967 2 2 297 462 -967 ...</PRE></TD></TR></TABLE></DIV><BR><P> `<SMALL>FILE_NAME.ANN' : </SMALL> This file contains P-num information for aparticular <!-- MATH: $\Delta \Delta G$ --><IMG WIDTH="42" HEIGHT="15" ALIGN="BOTTOM" BORDER="0" SRC="img9.gif" ALT="$\Delta \Delta G$">.The <I>i</I><SUP><I>th</I></SUP> record contains <I>i</I> and<!-- MATH: $P\!-\!num(i)$ --><IMG WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0" SRC="img107.gif" ALT="$P\!-\!num(i)$">.This file is used for annotating plotted structures.<P> `<SMALL>FILE_NAME.H-NUM' : </SMALL> This file is the same as`file_name.plot', except that the ``energy'' column is replaced by an``h-num'' column. These files are usually sorted by h-num; lowest tohighest, or best determined to worst determined. Often, only helicesin optimal foldings are retained. Figure <A HREF="node10.html#H-NUM">10</A> shows part of asorted and filtered h-num file corresponding to the plot file inFigure <A HREF="node10.html#PLOT">9</A>.<BR><DIV ALIGN="CENTER"><A NAME="H-NUM"> </A><A NAME="830"> </A><TABLE WIDTH="50%" BORDER=5 CELLPADDING=10><CAPTION><STRONG>Figure 10:</STRONG>The beginning and end of an h-num file sorted byh-num and filtered to include only helices in optimal foldings.As with P-num, H-num values are relative to a particular sequence andfree energy increment.</CAPTION><TR><TD BGCOLOR=#FFFFFF><PRE> level length istart jstart h-num 1 4 38 194 6.8 1 4 215 232 7.3 1 5 31 201 8.4 1 7 53 185 8.4 1 2 47 189 11.0 1 8 206 242 11.9 1 6 61 176 13.7 1 4 89 163 13.8 1 3 255 271 14.0 1 3 104 145 15.0 1 1 68 79 16.0 1 4 121 131 17.0 1 6 288 472 17.3 ... 1 2 353 389 35.0 1 3 364 377 38.7 1 3 297 459 39.0</PRE></TD></TR></TABLE></DIV><BR><P> `<SMALL>FILE_NAME.PS' : </SMALL> This is a PostScript file of the <I>energy dot plot</I> .<P> `<SMALL>FILE_NAME.GIF' : </SMALL> This is an image of the <I>energy dot plot</I> in ``gif''format, suitable for display on web pages.<P><HR><!--Navigation Panel--><A NAME="tex2html175" HREF="node11.html"><IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="img/next_motif.gif"></A> <A NAME="tex2html172" HREF="node9.html"><IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="img/up_motif.gif"></A> <A NAME="tex2html166" HREF="node9.html"><IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="img/previous_motif.gif"></A> <A NAME="tex2html174" HREF="node1.html"><IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="img/contents_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html176" HREF="node11.html">Optimal and suboptimal foldings</A><B> Up:</B> <A NAME="tex2html173" HREF="node9.html">OUTPUT</A><B> Previous:</B> <A NAME="tex2html167" HREF="node9.html">OUTPUT</A><!--End of Navigation Panel--><ADDRESS><TABLE><TR><TD><IMG SRC=img/shield16.gif HSPACE=20></TD><TD><I>Michael Zuker <BR>Institute for Biomedical Computing<BR>Washington University in St. Louis<BR>1998-12-05</I></TD></TR></TABLE></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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