<?xml version=“1.0” ?> <!DOCTYPE article SYSTEM “archivearticle.dtd”> <article> <front> <?mtl hellip?> <!– preformatted text, a code sample –> <article-meta> <title-group>
<article-title>Free energy reconstruction from nonequilibrium
single-molecule pulling experiments</article-title> </title-group> <contrib-group>
<contrib contrib-type="author"> <name> <surname>Hummer</surname> <given-names>Gerhard</given-names> </name> </contrib> <contrib contrib-type="author"> <name> <surname>Szabo</surname> <given-names>Attila</given-names> </name> <aff>Laboratory of Chemical Physics, National Institute of
Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520</aff>
</contrib> </contrib-group>
<permissions>
<copyright-statement>Copyright © 2001, The National Academy
of Sciences</copyright-statement> <copyright-year>2001</copyright-year> </permissions>
<related-article xmlns:xlink="http://www.w3.org/1999/xlink"
xhref=“11274379” related-article-type=“commentary” vol=“98” page=“3636”>See commentary on page 3636.</related-article>
<abstract> <p>Laser tweezers and atomic force microscopes are increasingly
used to probe the interactions and mechanical properties of individual molecules. Unfortunately, using such time-dependent perturbations to force rare molecular events also drives the system away from equilibrium. Nevertheless, we show how equilibrium free energy profiles can be extracted rigorously from repeated nonequilibrium force measurements on the basis of an extension of Jarzynski's remarkable identity between free energies and the irreversible work.</p>
</abstract>
</article-meta> <?mtl /hellip?> </front> <body> <?mtl hellip?><?mtl /hellip?> <p><?mtl hellip?><?mtl /hellip?> This can be seen in the following summation: <mml:math> <mml:semantics> <mml:mrow> <mml:munder> <mml:mo>∑</mml:mo> <mml:mi>m</mml:mi> </mml:munder> <mml:mrow> <mml:msub> <mml:mover accent='true'> <mml:mi>p</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mi>m</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:mrow> </mml:semantics> </mml:math> </p> <p>Sample 1:
<mml:math overflow="scroll"> <mml:mi>G</mml:mi> </mml:math> over <mml:math overflow="scroll"> <mml:mi>Σ</mml:mi> </mml:math> and <mml:math overflow="scroll"> <mml:mover><mml:mi>Σ</mml:mi><mml:mo>¯</mml:mo></mml:mover> </mml:math></p>
<p>Sample 2:
<mml:math overflow="scroll"> <mml:mi>N</mml:mi> </mml:math>, with <mml:math overflow="scroll"> <mml:mover><mml:mi>Σ</mml:mi><mml:mo>¯</mml:mo></mml:mover> </mml:math> being a disjoint copy of <mml:math overflow="scroll"> <mml:mi>Σ</mml:mi> </mml:math></p>
<p>Sample 3:
<mml:math overflow="scroll"> <mml:mi>Σ</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced open="{" close="}"> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>⋯</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math></p>
<p>Sample 4:
<mml:math overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>⋯</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:msub> </mml:mrow> </mml:math></p>
<p>Sample 5:
<mml:math display="block" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>⁢</mml:mo> <mml:msup> <mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:msub> <mml:mo>|</mml:mo> <mml:mi>⋯</mml:mi> <mml:mo>|</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>*</mml:mo> </mml:msup> <mml:mo>⁢</mml:mo> <mml:msub><mml:mover><mml:mi>a</mml:mi><mml:mo>¯</mml:mo></mml:mover> <mml:mi>i</mml:mi> </mml:msub> <mml:mtext>  </mml:mtext> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>i</mml:mi> <mml:mo><</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> <mml:mtext>.</mml:mtext> </mml:mrow> </mml:math></p>
<p>Sample 6:
<mml:math overflow="scroll"> <mml:msup> <mml:mfenced><mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:msub> <mml:mo>|</mml:mo> <mml:mi>⋯</mml:mi> <mml:mo>|</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:msub> </mml:mrow> </mml:mfenced> <mml:mo>*</mml:mo> </mml:msup> </mml:math></p>
<p>Sample 7:
<mml:math overflow="scroll"> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:mi>a</mml:mi> <mml:mo>⁢</mml:mo> <mml:msub> <mml:mi fontstyle="normal">L</mml:mi> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi>a</mml:mi> </mml:mrow> </mml:msub> <mml:mo>⁢</mml:mo><mml:mover><mml:mi>a</mml:mi><mml:mo>¯</mml:mo></mml:mover> </mml:math></p>
<p>Sample 8:
<mml:math overflow="scroll"> <mml:mi>X</mml:mi> <mml:mo>→</mml:mo> <mml:mi>a</mml:mi> <mml:mo>⁢</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>⋯</mml:mi> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>⁢</mml:mo><mml:mover><mml:mi>a</mml:mi><mml:mo>¯</mml:mo></mml:mover> </mml:math></p>
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