ÐÏ à¡± á > þÿ f h þÿÿÿ c d e u ÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿì¥Á #` ø ¿ ¸‘ bjbj¡ ¡ ;´ Õ Õ ÿÿ °@ ô 0º 2 ¤ Ä@ Ä@ ™ $ L“ $ L“ $ L“ 8 ÿÿ $ „“ | °@ – ÿÿ °@ n — D D™ ( l™ l™ l™ #› #› #› Ï Ñ Ñ Ñ Ñ Ñ Ñ $ h v õ e › #› Ÿ• °@ Ÿ• Ÿ• õ - $ $ l™ l™ ³ Z m¦ ’ Ï m¦ m¦ m¦ Ÿ• æ $ Ž) l™ °@ l™ = Ÿ• m¦ m¦ ª Sµ | ²0 ˶ þ °@ l™ ô– ÐÖ ž È L“ …£ r ϵ , p 0 $ áµ ê ˶ ˶ ’ – – °@ ÷¤ ]¹ – ´M #› #› Z }› #› @ m¦ #› ½› õ 4 ñ› ® õ ¦ #› #› #› ^ Ÿ• Ÿ• Ÿ• Ÿ• Ä@ Ä@ Ä@ dH $ Ä@ $ Ä@ $ Ä@ $ (‰ $ Ä@ ÿÿÿÿ Ä@ Ä@ $ $ (‰ Class ification: Biological Sciences: Biophysics Title: Single-Molecule Non-equilibrium Periodic Mg2+-Concentration Jump Experiments Reveal Details of the Early Folding Pathways of a Large RNA Author Information: Xiaohui Qu1,4, Glenna J. Smith2,4, Kang Taek Lee2,4, Tobin R. Sosnick3,4, Tao Pan3 and Norbert F. Scherer2,4* Departments of 1Physics, 2Chemistry, 3Biochemistry and Molecular Biology, and 4Institute for Biophysical Dynamics, University of Chicago, Chicago, IL 60637 *To whom correspondence should be addressed. E-mail: HYPERLINK "mailto:[email protected]" [email protected] . Author contributions: X.Q., G.S., K.T.L., T. RN.F.S. designed research; X.Q. performed research; X.Q. analyzed data; X.Q., N.F.S. wrote the paper Manuscript Information: Number of text pages (with references and figure legends): 20, double spaced, font size 11. Number of figures: 5 (single column, full width) Number of tables: 1 Character counts: 47039 with spaces Abbreviations: CthermoL18, the 260-residue catalytic domain of the RNase P RNA from Bacillus stearothermophilus, labeled with a FRET pair on the 3’ end and L18 loop; FRET, fluorescence resonance energy transfer; EFRET, efficiency of FRET, defined as EFRET = IA/( IA+ID), where IA and ID are the acceptor and donor fluorescence; [Mg2+], Mg2+ concentration; DOF, degrees of freedom. Keywords: RNA folding; FRET; single molecule; buffer jump; electrostatic relaxation; hidden degrees of freedom; memory; cooperativity. Abstract The evolution of RNA conformation with Mg2+ concentration (i.e., [Mg2+]) is typically determined from equilibrium titration measurements or nonequilibrium measurements with a single [Mg2+]-jump. Here, the folding of single RNA molecules is measured in response to a series of periodic changes of the Mg2+ concentration. The 260-residue catalytic domain of the RNase P RNA from Bacillus stearothermophilus is immobilized in a microfluidic flow chamber and the RNA conformational changes are probed by fluorescence resonance energy transfer (FRET). The kinetics of population redistribution after a [Mg2+]-jump and the observed connectivity of FRET states reveal details of the RNA folding pathway that complement and transcend the information available from equilibrium single molecule measurements. The FRET trajectories for jumps from [Mg2+]=0.01 to 0.1mM exhibit 2-state behavior in both directions, whereas jumps from 0.01mM to e"0 . 4 m M e x h i b i t t w o - s t a t e u n f o l d i n g b u t m u l t i - s t a t e f o l d i n g b e h a v i o r . T h e R N A m o l e c u l e s i n t h e t w o d i f f e r e n t c o n f o r m a t i o n s ( i . e . t h e l o w a n d h i g h F R E T s t a t e s ) p r i o r t o t h e [ M g 2 + ] i n c r e a s e a r e o b s e r v e d t o u n d e r g o d y n a m i c s i n t w o d i s t i n c t r e g i o n s o f t h e f r e e energy landscape that are separated by a high barrier; that is, each single molecules’ behavior is only infrequently changing on the > 10 min measurement time. We describe the RNA structural changes involved in crossing this barrier as a “hidden” degree of freedom because the changes do not alter the detected FRET value, but do alter the observed dynamics and kinetics. The FRET state populations do not achieve their equilibrium values at the end of the 5-10 sec [Mg2+] intervals due to the long memory of the “hidden” degrees of freedom, thereby creating a non-equilibrium steady-state condition. This allows probing regions of the free energy landscape that are infrequently sampled in equilibrium or single-jump measurements. Because the period of [Mg2+]-jumps is adjustable, regions of the free energy landscape that are virtually inaccessible in standard equilibrium measurements or single-jump experiments can be interrogated in the periodic [Mg2+]-jump experiments. Introduction RNA molecules perform both regulatory and catalytic functions ADDIN EN.CITE <EndNote><Cite><Author>Alberts</Author><Year>2002</Year><RecNum>23</RecNu m><record><rec-number>23</rec-number><ref-type name="Book">6</reftype><contributors><authors><author>Alberts, Bruce</author></authors></contributors><titles><title>Molecular biology of the cell</title></titles><pages>xxxiv, [1548] p.</pages><edition>4th</edition><keywords><keyword>Cytology.</keyword><ke yword>Molecular biology.</keyword><keyword>Cells.</keyword><keyword>Molecular Biology.</keyword></keywords><dates><year>2002</year></dates><publocation>New York</pub-location><publisher>Garland Science</publisher><isbn>0815332181 (hardbound)
0815340729 (pbk.)</isbn><call-num>See Reference Staff. By Appt in Jefferson Main RR (MRC) QH581.2 .M64 2002
See Reference Staff. By Appt in Jefferson Main RR (MRC) QH581.2 .M64 2002</call-num><urls><relatedurls><url>http://www.loc.gov/catdir/enhancements/fy0652/2001054471-d.html </url></related-urls></urls></record></Cite></EndNote> (1) . Hence, adopting the proper conformation(s) is crucial for their function. Determining the mechanisms by which RNA searches for and finds the proper tertiary structure (i.e. native state) remains a challenging problem ADDIN EN.CITE <EndNote><Cite><Author>Lilley</Author><Year>2005</Year><RecNum>25</RecNum ><record><rec-number>25</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Lilley, D. M. J.</author></authors></contributors><auth-address>Lilley, DMJ
Univ Dundee, Canc Res UK Nucl Acid Struct Res Grp, MSI WTB Complex, Dundee DD1 5EH, Scotland
Univ Dundee, Canc Res UK Nucl Acid Struct Res Grp, Dundee DD1 5EH, Scotland</auth-address><titles><title>Structure, folding and mechanisms of ribozymes</title><secondary-title>Current Opinion in Structural Biology</secondary-title></titles><periodical><fulltitle>Current Opinion in Structural Biology</full-title><abbr-1>Curr. Opin. Struct. Biol.</abbr-1><abbr-2>Curr Opin Struct Biol</abbr2></periodical><pages>313323</pages><volume>15</volume><number>3</number><keywords><keyword>peptid e-bond formation</keyword><keyword>delta virus ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>natural hammerhead ribozyme</keyword><keyword>catalytic metalion</keyword><keyword>acid-base catalysis</keyword><keyword>hairpin ribozyme</keyword><keyword>active-site</keyword><keyword>crystalstructure</keyword><keyword>tetrahymena ribozyme</keyword></keywords><dates><year>2005</year><pubdates><date>Jun</date></pub-dates></dates><isbn>0959440X</isbn><accession-num>ISI:000230381600011</accessionnum><urls><related-urls><url><Go to ISI>://000230381600011</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (2) . Cations, such as Mg2+, are essential to the RNA folding process; nonspecifically bound cations neutralize the highly charged RNA phosphate backbone while specifically bound cations help form and stabilize tertiary interactions and structures ADDIN EN.CITE <EndNote><Cite><Author>Draper</Author><Year>2005</Year><RecNum>24</RecNum ><record><rec-number>24</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Draper, D. E.</author><author>Grilley, D.</author><author>Soto, A. M.</author></authors></contributors><auth-address>Draper, DE
Johns Hopkins Univ, Dept Chem, Charles & 34Th St, Baltimore, MD 21218 USA
Johns Hopkins Univ, Dept Chem, Baltimore, MD 21218 USA
Johns Hopkins Univ, Program Mol & Computat Biophys, Baltimore, MD 21218 USA</auth-address><titles><title>Ions and RNA folding</title><secondarytitle>Annual Review of Biophysics and Biomolecular Structure</secondarytitle></titles><periodical><full-title>Annual Review of Biophysics and Biomolecular Structure</full-title><abbr-1>Annu. Rev. Biophys. Biomol. Struct.</abbr-1><abbr-2>Annu Rev Biophys Biomol Struct</abbr2></periodical><pages>221243</pages><volume>34</volume><keywords><keyword>magnesium</keyword><keyw ord>potassium</keyword><keyword>electrostatics</keyword><keyword>poissonboltzmann theory</keyword><keyword>hydration</keyword><keyword>phenylalanine transfer-rna</keyword><keyword>molecular-dynamics simulations</keyword><keyword>dimerization initiation site</keyword><keyword>x-ray-scattering</keyword><keyword>group-i intron</keyword><keyword>metal-ions</keyword><keyword>crystalstructure</keyword><keyword>nucleic-acids</keyword><keyword>tertiary structure</keyword><keyword>ribosomalrna</keyword></keywords><dates><year>2005</year></dates><isbn>10568700</isbn><accession-num>ISI:000230099600010</accessionnum><urls><related-urls><url><Go to ISI>://000230099600010</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Woo dson</Author><Year>2005</Year><RecNum>36</RecNum><record><recnumber>36</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Woodson, S. A.</author></authors></contributors><auth-address>Woodson, SA
Johns Hopkins Univ, TC Jenkins Dept Biophys, 3400 N Charles St, Baltimore, MD 21218 USA
Johns Hopkins Univ, TC Jenkins Dept Biophys, Baltimore, MD 21218 USA</auth-address><titles><title>Metal ions and RNA folding: a highly charged topic with a dynamic future</title><secondarytitle>Current Opinion in Chemical Biology</secondarytitle></titles><periodical><full-title>Current Opinion in Chemical Biology</full-title><abbr-1>Curr. Opin. Chem. Biol.</abbr-1><abbr-2>Curr Opin Chem Biol</abbr-2></periodical><pages>104109</pages><volume>9</volume><number>2</number><keywords><keyword>delta virus ribozyme</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>conformational switch</keyword><keyword>electrostatic properties</keyword><keyword>counterion condensation</keyword><keyword>thermodynamic framework</keyword><keyword>poisson-boltzmann</keyword><keyword>crystalstructure</keyword><keyword>nucleicacids</keyword></keywords><dates><year>2005</year><pubdates><date>Apr</date></pub-dates></dates><isbn>13675931</isbn><accession-num>ISI:000228607700003</accessionnum><urls><related-urls><url><Go to ISI>://000228607700003</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (3, 4) . The electrostatic and hydrogen-bond (base pairing) interactions create a free energy landscape that determines both the conformational search process and the dynamics related to function. The free energy landscape of RNA is, in general, believed to be more rugged than that for proteins; it has been shown that protein dynamics/kinetics are power law distributed whereas RNA have been shown to exhibit discrete behavior ADDIN EN.CITE <EndNote><Cite><Author>Thirumalai</Author><Year>2005</Year><RecNum>43</Re cNum><record><rec-number>43</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Thirumalai, D.</author><author>Hyeon, C.</author></authors></contributors><authaddress>Thirumalai, D
Univ Maryland, Inst Phys Sci & Technol, Biophys Program, College Pk, MD 20742 USA
Univ Maryland, Inst Phys Sci & Technol, Biophys Program, College Pk, MD 20742 USA
Univ Maryland, Inst Phys Sci & Technol, Dept Chem & Biochem, College Pk, MD 20742 USA</auth-address><titles><title>RNA and protein folding: Common themes and variations</title><secondarytitle>Biochemistry</secondary-title></titles><periodical><fulltitle>Biochemistry</full-title><abbr-1>Biochemistry</abbr-1><abbr2>Biochemistry</abbr-2></periodical><pages>49574970</pages><volume>44</volume><number>13</number><keywords><keyword>self -splicing rna</keyword><keyword>group-i ribozyme</keyword><keyword>single-domain proteins</keyword><keyword>helix-coil transition</keyword><keyword>offlattice models</keyword><keyword>tetrahymena ribozyme</keyword><keyword>secondary structure</keyword><keyword>tertiary structure</keyword><keyword>energy landscape</keyword><keyword>kinetic traps</keyword></keywords><dates><year>2005</year><pub-dates><date>Apr 5</date></pub-dates></dates><isbn>0006-2960</isbn><accessionnum>ISI:000228099000001</accession-num><urls><related-urls><url><Go to ISI>://000228099000001</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Gru ebele</Author><Year>2002</Year><RecNum>44</RecNum><record><recnumber>44</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Gruebele, M.</author></authors></contributors><auth-address>Gruebele, M
Univ Illinois, Dept Chem, 1209 W Calif St, Urbana, IL 61801 USA
Univ Illinois, Dept Chem, Urbana, IL 61801 USA
Univ Illinois, Dept Phys, Urbana, IL 61801 USA
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Univ British Columbia, Dept Phys & Astron, 6224 Agr Rd, Vancouver, BC V6T 1Z1, Canada
Univ Calif San Diego, Dept Phys, La Jolla, CA 92093 USA</auth-address><titles><title>Understanding protein folding with energy landscape theory - Part I: Basic concepts</title><secondary-title>Quarterly Reviews of Biophysics</secondary-title></titles><periodical><full-title>Quarterly Reviews of Biophysics</full-title><abbr-1>Q. Rev. Biophys.</abbr-1><abbr2>Q Rev Biophys</abbr-2></periodical><pages>111167</pages><volume>35</volume><number>2</number><keywords><keyword>molecu lar-dynamics simulations</keyword><keyword>transition-state ensemble</keyword><keyword>replica symmetrybreaking</keyword><keyword>small globularproteins</keyword><keyword>amino-acid-sequences</keyword><keyword>spinglass models</keyword><keyword>block co-polymers</keyword><keyword>betalactoglobulin</keyword><keyword>statisticalmechanics</keyword><keyword>chymotrypsin inhibitor2</keyword></keywords><dates><year>2002</year><pubdates><date>May</date></pub-dates></dates><isbn>00335835</isbn><accession-num>ISI:000177476300001</accessionnum><urls><related-urls><url><Go to ISI>://000177476300001</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Smi th</Author><Year>2007</Year><RecNum>14</RecNum><record><recnumber>14</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Smith, G., Lee, K.-T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite><Cite><Author>Russell</Author><Year>2002</Year><RecNum>11</RecNum> <record><rec-number>11</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Russell, R.</author><author>Zhuang, X. W.</author><author>Babcock, H. P.</author><author>Millett, I. S.</author><author>Doniach, S.</author><author>Chu, S.</author><author>Herschlag, D.</author></authors></contributors><auth-address>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Stanford, CA 94305 USA
Stanford Univ, Dept Chem, Stanford, CA 94305 USA
Stanford Univ, Dept Appl Phys, Stanford, CA 94305 USA</authaddress><titles><title>Exploring the folding landscape of a structured RNA</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr- 1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>155160</pages><volume>99</volume><number>1</number><keywords><keyword>selfsplicing rna</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>catalytic rna</keyword><keyword>secondary structure</keyword><keyword>energy landscape</keyword><keyword>escherichia-coli</keyword><keyword>ribosomalrna</keyword><keyword>kinetic traps</keyword><keyword>pathways</keyword><keyword>molecule</keyword></ke ywords><dates><year>2002</year><pub-dates><date>Jan 8</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000173233300031</accession-num><urls><related-urls><url><Go to ISI>://000173233300031</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Guo </Author><Year>2005</Year><RecNum>51</RecNum><record><rec-number>51</recnumber><ref-type name="Book Section">5</reftype><contributors><authors><author>Guo, W.</author><author>Shea, J. E.</author><author>Berry, R. S.</author></authors></contributors><titles><title>The physics of the interactions governing folding and association of proteins</title><secondary-title>Cell Injury: Mechanisms, Responses, and Repair</secondary-title><tertiary-title>Annals of the New York Academy of Sciences</tertiary-title></titles><pages>3453</pages><volume>1066</volume><dates><year>2005</year></dates><accession -num>ISI:000236999100003</accession-num><urls><related-urls><url><Go to ISI>://000236999100003</url></relatedurls></urls></record></Cite></EndNote> (5-10) . In equilibrium measurements, which are carried out under constant buffer conditions, the RNA molecules are in equilibrium with the environment; only spontaneous conformational fluctuations associated with thermal motion are observed. While the region near the minimum of the free energy landscape is probed in equilibrium measurements, non-equilibrium concentration-jump experiments probe a larger region as the molecules move farther from their initial equilibrium conformation(s). The non-equilibrium relaxation to new conformations reveals the pathway(s) the RNA molecules take to the new minimum free energy state. Ensemble concentration-jump measurements using rapid mixing techniques have been widely applied to study RNA and protein folding ADDIN EN.CITE <EndNote><Cite><Author>Eigen</Author><Year>1960</Year><RecNum>18</RecNum> <record><rec-number>18</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Eigen, M.</author><author>Hammes, G. G.</author></authors></contributors><titles><title>Kinetic Studies of Adp Reactions with the Temperature Jump Method</title><secondarytitle>Journal of the American Chemical Society</secondarytitle></titles><periodical><full-title>Journal of the American Chemical Society</full-title><abbr-1>J. Am. Chem. Soc.</abbr-1><abbr-2>J Am Chem Soc</abbr-2></periodical><pages>59515952</pages><volume>82</volume><number>22</number><dates><year>1960</year ></dates><isbn>0002-7863</isbn><accessionnum>ISI:A1960WB34900041</accession-num><urls><related-urls><url><Go to ISI>://A1960WB34900041</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Mun oz</Author><Year>1997</Year><RecNum>19</RecNum><record><rec- number>19</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Munoz, V.</author><author>Thompson, P. A.</author><author>Hofrichter, J.</author><author>Eaton, W. A.</author></authors></contributors><auth-address>Munoz, V
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Univ Chicago, Dept Biochem & Mol Biol, 920 E 58th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA</auth-address><titles><title>Distinguishing between two-state and three-state models for ubiquitin folding</title><secondary-title>Biochemistry</secondarytitle></titles><periodical><full-title>Biochemistry</full-title><abbr1>Biochemistry</abbr-1><abbr-2>Biochemistry</abbr2></periodical><pages>1169611701</pages><volume>39</volume><number>38</number><keywords><keyword>hyd rogen-exchange</keyword><keyword>transitionstate</keyword><keyword>kinetics</keyword><keyword>molecules</keyword><ke yword>mechanism</keyword><keyword>proteins</keyword><keyword>domain</keyw ord></keywords><dates><year>2000</year><pub-dates><date>Sep 26</date></pub-dates></dates><isbn>0006-2960</isbn><accessionnum>ISI:000089596200019</accession-num><urls><related-urls><url><Go to ISI>://000089596200019</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Fan g</Author><Year>1999</Year><RecNum>47</RecNum><record><recnumber>47</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Fang, X. W.</author><author>Pan, T.</author><author>Sosnick, T. R.</author></authors></contributors><authaddress>Pan, T
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA</auth-address><titles><title>Mg2+-dependent folding of a large ribozyme without kinetic traps</title><secondary-title>Nature Structural Biology</secondary-title></titles><periodical><full-title>Nature Structural Biology</full-title><abbr-1>Nature Struct. Biol.</abbr1><abbr-2>Nature Struct Biol</abbr-2></periodical><pages>10911095</pages><volume>6</volume><number>12</number><keywords><keyword>group -i ribozyme</keyword><keyword>rnasep</keyword><keyword>proteins</keyword></keywords><dates><year>1999</year> <pub-dates><date>Dec</date></pub-dates></dates><isbn>10728368</isbn><accession-num>ISI:000084022300007</accession- num><urls><related-urls><url><Go to ISI>://000084022300007</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Rus sell</Author><Year>2002</Year><RecNum>49</RecNum><record><recnumber>49</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Russell, R.</author><author>Millettt, I. S.</author><author>Tate, M. W.</author><author>Kwok, L. W.</author><author>Nakatani, B.</author><author>Gruner, S. M.</author><author>Mochrie, S. G. J.</author><author>Pande, V.</author><author>Doniach, S.</author><author>Herschlag, D.</author><author>Pollack, L.</author></authors></contributors><authaddress>Pollack, L
Cornell Univ, Sch Appl & Engn Phys, Dept Phys, Ithaca, NY 14853 USA
Cornell Univ, Sch Appl & Engn Phys, Dept Phys, Ithaca, NY 14853 USA
Cornell Univ, CHESS, Ithaca, NY 14853 USA
Stanford Univ, Dept Biochem, Stanford, CA 94305 USA
Stanford Univ, Dept Chem, Stanford, CA 94305 USA
Stanford Univ, Dept Phys & Appl Phys, Stanford, CA 94305 USA
Yale Univ, Dept Phys, New Haven, CT 06520 USA</auth-address><titles><title>Rapid compaction during RNA folding</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>42664271</pages><volume>99</volume><number>7</number><keywords><keyword>xray-scattering</keyword><keyword>tetrahymena ribozyme</keyword><keyword>state</keyword><keyword>pathways</keyword><key word>substrate</keyword><keyword>molecule</keyword><keyword>collapse</key word><keyword>domain</keyword></keywords><dates><year>2002</year><pubdates><date>Apr 2</date></pub-dates></dates><isbn>00278424</isbn><accession-num>ISI:000174856000027</accessionnum><urls><related-urls><url><Go to ISI>://000174856000027</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Dow ney</Author><Year>2006</Year><RecNum>59</RecNum><record><recnumber>59</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Downey, C. D.</author><author>Fiore, J. L.</author><author>Stoddard, C. D.</author><author>Hodak, J. H.</author><author>Nesbitt, D. J.</author><author>Pardi, A.</author></authors></contributors><auth-address>Pardi, A
Univ Colorado, Natl Inst Stand & Technol, Dept Chem & Biochem, 215 UCB, Boulder, CO 80309 USA
Univ Colorado, Natl Inst Stand & Technol, Dept Chem & Biochem, Boulder, CO 80309 USA
Univ Colorado, Natl Inst Stand & Technol, JILA, Boulder, CO 80309 USA</auth-address><titles><title>Metal ion dependence, thermodynamics, and kinetics for intramolecular docking of a GAAA tetraloop and receptor connected by a flexible linker</title><secondarytitle>Biochemistry</secondary-title></titles><periodical><fulltitle>Biochemistry</full-title><abbr-1>Biochemistry</abbr-1><abbr2>Biochemistry</abbr-2></periodical><pages>36643673</pages><volume>45</volume><number>11</number><keywords><keyword>p4p6 rna domain</keyword><keyword>group-i</keyword><keyword>tetrahymena ribozyme</keyword><keyword>hairpin ribozyme</keyword><keyword>hammerhead ribozyme</keyword><keyword>tertiary structure</keyword><keyword>crystal- structure</keyword><keyword>transition-state</keyword><keyword>singlemolecule</keyword><keyword>ribonucleasep</keyword></keywords><dates><year>2006</year><pub-dates><date>Mar 21</date></pub-dates></dates><isbn>0006-2960</isbn><accessionnum>ISI:000236320400022</accession-num><urls><related-urls><url><Go to ISI>://000236320400022</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (1116) . The population relaxation process is assumed to be well described by the Fluctuation-Dissipation Theorem, that, together with detailed balance, allows determination of the equilibrium rate constants ADDIN EN.CITE <EndNote><Cite><Author>Chandler</Author><Year>1987</Year><RecNum>15</RecN um><record><rec-number>15</rec-number><ref-type name="Book">6</reftype><contributors><authors><author>Chandler, David</author></authors></contributors><titles><title>Introduction to modern statistical mechanics</title></titles><pages>xiii, 274 p.</pages><keywords><keyword>Statistical mechanics.</keyword><keyword>Statistical thermodynamics.</keyword><keyword>Chemistry, Physical and theoretical.</keyword></keywords><dates><year>1987</year></dates><publocation>New York</pub-location><publisher>Oxford University Press</publisher><isbn>019504276X (alk. paper)
0195042778 (pbk.)</isbn><call-num>Jefferson or Adams Bldg General or Area Studies Reading Rms QC174.8 .C47 1987
Main or Science/Business Reading Rms STORED OFFSITE QC174.8 .C47 1987</call-num><urls><relatedurls><url>http://www.loc.gov/catdir/enhancements/fy0602/86017950d.html</url><url>http://www.loc.gov/catdir/enhancements/fy0602/86017950t.html </url></related-urls></urls></record></Cite></EndNote> (17) . The measured ensemble-averaged kinetics allow constructing minimal kinetic schemes to describe folding or unfolding. Single-molecule fluorescence resonance energy transfer (FRET) measurements of surface immobilized RNA have been a powerful approach for studying equilibrium conformational dynamics of DNA and RNA ADDIN EN.CITE <EndNote><Cite><Author>McKinney</Author><Year>2005</Year><RecNum>57</RecN um><record><rec-number>57</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>McKinney, S. A.</author><author>Freeman, A. D. J.</author><author>Lilley, D. M. J.</author><author>Ha, T. J.</author></authors></contributors><authaddress>Ha, Tj
Univ Illinois, Dept Phys, 1110 W Green St, Urbana, IL 61801 USA
Univ Illinois, Dept Phys, Urbana, IL 61801 USA
Univ Dundee, Dept Biochem, Canc Res UK, Nucl Acid Res Struct Grp, Dundee DD1 5EH, Scotland</auth-address><titles><title>Observing spontaneous branch migration of Holliday junctions one step at a time</title><secondarytitle>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><fulltitle>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr-1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr2></periodical><pages>57155720</pages><volume>102</volume><number>16</number><keywords><keyword>fre t</keyword><keyword>single molecule</keyword><keyword>recombination</keyword><keyword>DNA structure</keyword><keyword>4-way DNA junction</keyword><keyword>single- molecule</keyword><keyword>sequence dependence</keyword><keyword>crystalstructure</keyword><keyword>nucleicacids</keyword><keyword>recombination</keyword><keyword>spectroscopy</key word><keyword>replication</keyword><keyword>conformers</keyword><keyword> proteins</keyword></keywords><dates><year>2005</year><pub-dates><date>Apr 19</date></pub-dates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000228565200017</accession-num><urls><related-urls><url><Go to ISI>://000228565200017</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Cos a</Author><Year>2006</Year><RecNum>56</RecNum><record><recnumber>56</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Cosa, G.</author><author>Zeng, Y. N.</author><author>Liu, H. W.</author><author>Landes, C. F.</author><author>Makarov, D. E.</author><author>Musier-Forsyth, K.</author><author>Barbara, P. F.</author></authors></contributors><authaddress>Barbara, PF
Univ Texas, Ctr Nano & Mol Sci & Technol, Dept Chem & Biochem, Austin, TX 78712 USA
Univ Texas, Ctr Nano & Mol Sci & Technol, Dept Chem & Biochem, Austin, TX 78712 USA
Univ Minnesota, Dept Chem, Minneapolis, MN 55455 USA</authaddress><titles><title>Evidence for non-two-state kinetics in the nucleocapsid protein chaperoned opening of DNA hairpins</title><secondary-title>Journal of Physical Chemistry B</secondary-title></titles><periodical><full-title>Journal of Physical Chemistry B</full-title></periodical><pages>24192426</pages><volume>110</volume><number>5</number><keywords><keyword>nucl eic-acid-chaperone</keyword><keyword>plus-strand transfer</keyword><keyword>single-molecule</keyword><keyword>reverse transcription</keyword><keyword>conformational fluctuations</keyword><keyword>transferrna</keyword><keyword>binding</keyword><keyword>dynamics</keyword><keywor d>spectroscopy</keyword><keyword>heterogeneity</keyword></keywords><dates ><year>2006</year><pub-dates><date>Feb 9</date></pubdates></dates><isbn>1520-6106</isbn><accessionnum>ISI:000235284300067</accession-num><urls><related-urls><url><Go to ISI>://000235284300067</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Zhu ang</Author><Year>2005</Year><RecNum>9</RecNum><record><recnumber>9</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Zhuang, X. W.</author></authors></contributors><auth-address>Zhuang, XW
Harvard Univ, Dept Chem & Biol Chem, Cambridge, MA 02138 USA
Harvard Univ, Dept Chem & Biol Chem, Cambridge, MA 02138 USA
Harvard Univ, Dept Phys, Cambridge, MA 02138 USA</authaddress><titles><title>Single-molecule RNA science</title><secondarytitle>Annual Review of Biophysics and Biomolecular Structure</secondarytitle></titles><periodical><full-title>Annual Review of Biophysics and Biomolecular Structure</full-title><abbr-1>Annu. Rev. Biophys. Biomol. Struct.</abbr-1><abbr-2>Annu Rev Biophys Biomol Struct</abbr2></periodical><pages>399414</pages><volume>34</volume><keywords><keyword>single-molecule experiments</keyword><keyword>rna folding</keyword><keyword>rna catalysis</keyword><keyword>fluorescence resonance energy transfer</keyword><keyword>optical tweezers</keyword><keyword>selfsplicing rna</keyword><keyword>fluorescence correlation spectroscopy</keyword><keyword>resonance energytransfer</keyword><keyword>hairpin ribozyme</keyword><keyword>thermophila ribozyme</keyword><keyword>structural dynamics</keyword><keyword>tertiary structure</keyword><keyword>mechanical force</keyword><keyword>folding kinetics</keyword><keyword>transitionstate</keyword></keywords><dates><year>2005</year></dates><isbn>10568700</isbn><accession-num>ISI:000230099600017</accessionnum><urls><related-urls><url><Go to ISI>://000230099600017</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Rue da</Author><Year>2004</Year><RecNum>6</RecNum><record><rec-number>6</recnumber><ref-type name='Journal Article'>17</reftype><contributors><authors><author>Rueda, D.</author><author>Bokinsky, G.</author><author>Rhodes, M. M.</author><author>Rust, M. J.</author><author>Zhuang, X. W.</author><author>Walter, N. G.</author></authors></contributors><auth-address>Zhuang, XW
Harvard Univ, Dept Chem & Biol Chem, Cambridge, MA 02138 USA
Harvard Univ, Dept Chem & Biol Chem, Cambridge, MA 02138 USA
Harvard Univ, Dept Phys, Cambridge, MA 02138 USA
Univ Michigan, Dept Chem, Ann Arbor, MI 48109 USA</auth-address><titles><title>Single-molecule enzymology of RNA: Essential functional groups impact catalysis from a distance</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</fulltitle></periodical><pages>1006610071</pages><volume>101</volume><number>27</number><keywords><keyword>te rtiary structure formation</keyword><keyword>hairpin ribozyme</keyword><keyword>structural dynamics</keyword><keyword>mechanism</keyword></keywords><dates><year>200 4</year><pub-dates><date>Jul 6</date></pub-dates></dates><isbn>00278424</isbn><accession-num>ISI:000222534200023</accessionnum><urls><related-urls><url><Go to ISI>://000222534200023</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Dow ney</Author><Year>2006</Year><RecNum>59</RecNum><record><recnumber>59</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Downey, C. D.</author><author>Fiore, J. L.</author><author>Stoddard, C. D.</author><author>Hodak, J. H.</author><author>Nesbitt, D. J.</author><author>Pardi, A.</author></authors></contributors><auth-address>Pardi, A
Univ Colorado, Natl Inst Stand & Technol, Dept Chem & Biochem, 215 UCB, Boulder, CO 80309 USA
Univ Colorado, Natl Inst Stand & Technol, Dept Chem & Biochem, Boulder, CO 80309 USA
Univ Colorado, Natl Inst Stand & Technol, JILA, Boulder, CO 80309 USA</auth-address><titles><title>Metal ion dependence, thermodynamics, and kinetics for intramolecular docking of a GAAA tetraloop and receptor connected by a flexible linker</title><secondarytitle>Biochemistry</secondary-title></titles><periodical><fulltitle>Biochemistry</full-title><abbr-1>Biochemistry</abbr-1><abbr2>Biochemistry</abbr-2></periodical><pages>36643673</pages><volume>45</volume><number>11</number><keywords><keyword>p4p6 rna domain</keyword><keyword>group-i</keyword><keyword>tetrahymena ribozyme</keyword><keyword>hairpin ribozyme</keyword><keyword>hammerhead ribozyme</keyword><keyword>tertiary structure</keyword><keyword>crystalstructure</keyword><keyword>transition-state</keyword><keyword>singlemolecule</keyword><keyword>ribonucleasep</keyword></keywords><dates><year>2006</year><pub-dates><date>Mar 21</date></pub-dates></dates><isbn>0006-2960</isbn><accessionnum>ISI:000236320400022</accession-num><urls><related-urls><url><Go to ISI>://000236320400022</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (16, 18-21) . By contrast, only a few single-molecule concentration-jump experiments have been reported for RNA ADDIN EN.CITE <EndNote><Cite><Author>Ha</Author><Year>1999</Year><RecNum>13</RecNum><re cord><rec-number>13</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Ha, T.</author><author>Zhuang, X. W.</author><author>Kim, H. D.</author><author>Orr, J. W.</author><author>Williamson, J. R.</author><author>Chu, S.</author></authors></contributors><auth-address>Chu, S
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Scripps Res Inst, Dept Mol Biol, La Jolla, CA 92037 USA
Scripps Res Inst, Skaggs Inst Chem Biol, La Jolla, CA 92037 USA</auth-address><titles><title>Ligand-induced conformational changes observed in single RNA molecules</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</fulltitle><abbr-1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>90779082</pages><volume>96</volume><number>16</number><keywords><keyword>ribo somal-protein s15</keyword><keyword>resonance energytransfer</keyword><keyword>elongational flow</keyword><keyword>roomtemperature</keyword><keyword>dynamics</keyword><keyword>binding</keyword ><keyword>site</keyword></keywords><dates><year>1999</year><pubdates><date>Aug 3</date></pub-dates></dates><isbn>00278424</isbn><accession-num>ISI:000081835500056</accessionnum><urls><related-urls><url><Go to ISI>://000081835500056</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Zhu ang</Author><Year>2000</Year><RecNum>10</RecNum><record><recnumber>10</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Zhuang, X. W.</author><author>Bartley, L. E.</author><author>Babcock, H. P.</author><author>Russell, R.</author><author>Ha, T. J.</author><author>Herschlag, D.</author><author>Chu, S.</author></authors></contributors><auth-address>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Beckman Ctr B400, Stanford, CA 94305 USA</auth-address><titles><title>A single-molecule study of RNA catalysis and folding</title><secondarytitle>Science</secondary-title></titles><pages>20482051</pages><volume>288</volume><number>5473</number><keywords><keyword>t etrahymena-thermophila ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>activesite</keyword><keyword>substrate</keyword><keyword>binding</keyword><keyw ord>dynamics</keyword><keyword>titin</keyword><keyword>pathways</keyword> <keyword>protein</keyword><keyword>steps</keyword></keywords><dates><year >2000</year><pub-dates><date>Jun 16</date></pub-dates></dates><isbn>00368075</isbn><accession-num>ISI:000087687000052</accessionnum><urls><related-urls><url><Go to ISI>://000087687000052</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Rus sell</Author><Year>2002</Year><RecNum>11</RecNum><record><recnumber>11</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Russell, R.</author><author>Zhuang, X. W.</author><author>Babcock, H. P.</author><author>Millett, I. S.</author><author>Doniach, S.</author><author>Chu, S.</author><author>Herschlag, D.</author></authors></contributors><authaddress>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Stanford, CA 94305 USA
Stanford Univ, Dept Chem, Stanford, CA 94305 USA
Stanford Univ, Dept Appl Phys, Stanford, CA 94305 USA</auth-address><titles><title>Exploring the folding landscape of a structured RNA</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>155160</pages><volume>99</volume><number>1</number><keywords><keyword>selfsplicing rna</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>catalytic rna</keyword><keyword>secondary structure</keyword><keyword>energy landscape</keyword><keyword>escherichia-coli</keyword><keyword>ribosomalrna</keyword><keyword>kinetic traps</keyword><keyword>pathways</keyword><keyword>molecule</keyword></ke ywords><dates><year>2002</year><pub-dates><date>Jan 8</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000173233300031</accession-num><urls><related-urls><url><Go to ISI>://000173233300031</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Zhu ang</Author><Year>2000</Year><RecNum>10</RecNum><record><recnumber>10</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Zhuang, X. W.</author><author>Bartley, L. E.</author><author>Babcock, H. P.</author><author>Russell, R.</author><author>Ha, T. J.</author><author>Herschlag, D.</author><author>Chu, S.</author></authors></contributors><auth-address>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Beckman Ctr B400, Stanford, CA 94305 USA</auth-address><titles><title>A single-molecule study of RNA catalysis and folding</title><secondarytitle>Science</secondary-title></titles><pages>20482051</pages><volume>288</volume><number>5473</number><keywords><keyword>t etrahymena-thermophila ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>activesite</keyword><keyword>substrate</keyword><keyword>binding</keyword><keyw ord>dynamics</keyword><keyword>titin</keyword><keyword>pathways</keyword> <keyword>protein</keyword><keyword>steps</keyword></keywords><dates><year >2000</year><pub-dates><date>Jun 16</date></pub-dates></dates><isbn>00368075</isbn><accession-num>ISI:000087687000052</accession- num><urls><related-urls><url><Go to ISI>://000087687000052</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (9, 22, 23) . These experiments allowed construction of an RNA folding pathway. Here, we use FRET to observe the structural response of single RNA molecules to periodic Mg2+ concentration ([Mg2+]) jumps (Fig. 1-A) in order to study the folding of the 260-residue catalytic domain of the thermophilic RNase P RNA (termed CthermoL18; see ADDIN EN.CITE <EndNote><Cite><Author>Smith</Author><Year>2007</Year><RecNum>14</RecNum> <record><rec-number>14</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Smith, G., Lee, K.T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite><Cite><Author>Smith</Author><Year>2005</Year><RecNum>2</RecNum><re cord><rec-number>2</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Smith, G. J.</author><author>Sosnick, T. R.</author><author>Scherer, N. F.</author><author>Pan, T.</author></authors></contributors><auth-address>Scherer, NF
Univ Chicago, Dept Biochem & Mol Biol, 920 E 58Th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Univ Chicago, Dept Chem, Chicago, IL 60637 USA
Univ Chicago, Inst Biophys Dynam, Chicago, IL 60637 USA</authaddress><titles><title>Efficient fluorescence labeling of a large RNA through oligonucleotide hybridization</title><secondary-title>Rna-a Publication of the Rna Society</secondary-title></titles><pages>234239</pages><volume>11</volume><number>2</number><keywords><keyword>labeli ng</keyword><keyword>hybridization</keyword><keyword>fret</keyword><keywo rd>single molecule</keyword><keyword>singlemolecule</keyword><keyword>energytransfer</keyword><keyword>ribonuclease-p</keyword><keyword>secondary structure</keyword><keyword>substrate-binding</keyword><keyword>large ribozyme</keyword><keyword>sites</keyword><keyword>stability</keyword><ke yword>dynamics</keyword></keywords><dates><year>2005</year><pubdates><date>Feb</date></pub-dates></dates><isbn>13558382</isbn><accession-num>ISI:000226709500014</accessionnum><urls><related-urls><url><Go to ISI>://000226709500014</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (8, 24) and Supplementary Material for details). The kinetic scheme shown in Fig. 1-B illustrates the experiment: each [Mg2+]-jump induces a change of the free energy landscape upon which the RNA population subsequently redistributes. Alternating forward and reverse jumps create a cycle ADDIN EN.CITE <EndNote><Cite><Author>Hill</Author><Year>1989</Year><RecNum>60</RecNum>< record><rec-number>60</rec-number><ref-type name="Book">6</reftype><contributors><authors><author>Hill, Terrell L.</author><author>Hill, Terrell L.</author></authors></contributors><titles><title>Free energy transduction and biochemical cycle kinetics</title></titles><pages>119 p.</pages><keywords><keyword>Thermodynamics.</keyword><keyword>Gibbs&apos ; free energy.</keyword><keyword>Bioenergetics.</keyword></keywords><dates><year >1989</year></dates><pub-location>New York</publocation><publisher>SpringerVerlag</publisher><isbn>0387968369</isbn><call-num>Jefferson or Adams Bldg General or Area Studies Reading Rms QP517.T48 H55 1989</callnum><urls></urls></record></Cite></EndNote> (25) . When the period of the [Mg2+]-jumps is longer than the slowest relaxation process, the periodic [Mg2+]-jump measurement gives information equivalent to the single-jump experiment. However, when the [Mg2+]-jump period is shorter, the distribution of configurations of the RNA molecules prior to each [Mg2+]jump will be different compared to the single jump experiment. Therefore, such non-equilibrium steady-state measurements allow probing regions of the free energy landscape that may otherwise escape detection. For the experiments reported here, the full [Mg2+]-jump period is 20 sec; 10 sec each for the low and high [Mg2+] intervals. For CthermoL18, this period is too short for the system to achieve equilibrium prior to the next jump. This is observed with striking clarity in the kinetics of relaxation associated with each [Mg2+] interval. The range of [Mg2+]jumps employed, from 0.01mM (i.e., low [Mg2+ ] ) t o 0 . 1 , 0 . 4 , o r 1 . 0 m M ( i . e . , h i g h [ M g 2 + ] ) , a l l o w s p r o b i n g r e l a t i v e l y s i m p l e c o n f o r m a t i o n a l c h a n g e s ( i . e . t w o s t a t e b e h a v i o r a t 0 . 1 m M ) a n d c o m p l e x m u l t i - s t a t e b e h a v i o r ( a t e"0 . 4 m M ) . N o n s p e c i f i c e l e c t r o s t a t i c r e l a x a t i o n o f t h e R N A s t r u c t u r e i s o b s e r v e d d u ring each interval for all conditions. We observe exponential kinetics in each [Mg2+] interval but the relaxation at high [Mg2+] is not complete. Furthermore, by way of considering the FRET value just prior to the jump we identify conformations that are slowly interconverting and are termed “hidden degree(s) of freedom”. The species on either side of this barrier have indistinguishable FRET efficiency (EFRET) values but very different dynamics. Therefore, for single-molecule FRET measurements, the barrier functions as a “hidden” degree of freedom (DOF) that exhibits long memory of the RNA structure and hence influences the individual molecule’s dynamics and kinetics of population relaxation. Experimental Results Measurements were conducted at three [Mg2+]-jump conditions 0 a d c m u i t . n e o o n n r 0 d t n l f c a 1 ”!0 S u a i l f o r e c u o l d r e a j e c . p s m l i s t 4 p ) a e n e o , a n d l e m e n t . W e r t i o n a l s a f t e g , a n d a s f o r i e s a : 0 . 0 1 a r y e f e r c h a r a a f t l d i n r e s 0 . 0 1 ”!0 . ”!1 . 0 m M M a t e r i a t o t h e n g e s o f [ M g 2 + ] e r a [ M g . F o r egmented into 1 , ( s e e F i g . l f o r 1 R N A d e c r e a s e a s g 2 + ] a n a l y s i s , unfolding and folding intervals, and these intervals further separated into two cases according to whether the molecule occupied the low or high EFFRET state immediately prior to the [Mg2+]-jump, see Fig. 2 C1-C4. The averaged relaxation properties of the resulting four sorted sets (unfolding starting low EFRET, unfolding starting high EFRET, folding starting low EFRET, folding starting high EFRET) are calculated separately and yield key insights into the alternate folding pathways. We observed two classes of RNA conformational change: 1) discrete transitions characteristic of barrier-crossing events that are observed during each constant [Mg2+] interval, and 2) smooth transitions only observed during the 1 second [Mg2+] change. The smooth transitions track the [Mg2+] change (Fig. 3-A1 inset) during the [Mg2+]-mixing time in a manner consistent with electrostatic relaxation (i.e. collapse or expansion) of RNA structure. Two-State Unfolding and Folding for [Mg2+ ] = 0 . 0 1 ”!0 . 1 m M E F R E T t r a j e c t o r i e s ( F i g . 2 - A ) a n d c u m u l a t i v e E F R E T h i s t o g r a m s ( F i g . 2 B ) s h o w t h a t t h e R N A e x h i b i t s t w o s t a t e b e h a v i o r f o r b o t h u n f o l d i n g a n d f o l d i n g i n t h e 0 . 0 1 ”!0 . 1 m M e x p e r i m e n t . T w o - s t a t e b e h a v i o r i s c o n s i s t e n t w i t h t h e e x p e c t a t i o n f r o m o u r equilibrium study (Fig. 2 insets, and ref. ADDIN EN.CITE <EndNote><Cite><Author>Smith</Author><Year>2007</Year><RecNum>14</RecNum> <record><rec-number>14</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Smith, G., Lee, K.T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite></EndNote> (8) ). The high EFRET peak is more dominant in the folding interval (Fig. 2-B2) than in the unfolding interval (Fig. 2-B1), although it is apparent form the peak amplitudes that the population has not yet achieved equilibrium (Fig. 2-B2, inset). The kinetics of population relaxation are clearly asymmetric (e.g. different) depending on the initial EFRET state prior to the [Mg2+]jumps, and this asymmetry is especially apparent in the folding interval. If an RNA began it’s folding interval from a high EFRET state (Fig.2-C3), it tends to stay in the high EFRET state with a population relaxation time constant much longer than the 10 second jump interval. RNA folding from the low EFRET state (Fig.2-C4), on the other hand, relaxes relatively quickly, almost achieving equilibrium in 10 seconds. The longlived high EFRET state observed in the first case is obviously a different conformation than the actively fluctuating high EFRET state visited in the second case. These two high EFRET conformations, distinguished only by their kinetics, reveal a property that we call the “hidden” DOF in CthermoL18. The starting conformation immediately before a [Mg2+] change has a large effect on the subsequent kinetics and pathways. Sensitivity of the kinetic rate on initial state was observed in previous single jump studies ADDIN EN.CITE <EndNote><Cite><Author>Ha</Author><Year>1999</Year><RecNum>13</RecNum><re cord><rec-number>13</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Ha, T.</author><author>Zhuang, X. W.</author><author>Kim, H. D.</author><author>Orr, J. W.</author><author>Williamson, J. R.</author><author>Chu, S.</author></authors></contributors><auth-address>Chu, S
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Scripps Res Inst, Dept Mol Biol, La Jolla, CA 92037 USA
Scripps Res Inst, Skaggs Inst Chem Biol, La Jolla, CA 92037 USA</auth-address><titles><title>Ligand-induced conformational changes observed in single RNA molecules</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</fulltitle><abbr-1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>90779082</pages><volume>96</volume><number>16</number><keywords><keyword>ribo somal-protein s15</keyword><keyword>resonance energytransfer</keyword><keyword>elongational flow</keyword><keyword>roomtemperature</keyword><keyword>dynamics</keyword><keyword>binding</keyword ><keyword>site</keyword></keywords><dates><year>1999</year><pubdates><date>Aug 3</date></pub-dates></dates><isbn>00278424</isbn><accession-num>ISI:000081835500056</accessionnum><urls><related-urls><url><Go to ISI>://000081835500056</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Zhu ang</Author><Year>2000</Year><RecNum>10</RecNum><record><recnumber>10</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Zhuang, X. W.</author><author>Bartley, L. E.</author><author>Babcock, H. P.</author><author>Russell, R.</author><author>Ha, T. J.</author><author>Herschlag, D.</author><author>Chu, S.</author></authors></contributors><auth-address>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Beckman Ctr B400, Stanford, CA 94305 USA</auth-address><titles><title>A single-molecule study of RNA catalysis and folding</title><secondarytitle>Science</secondary-title></titles><pages>20482051</pages><volume>288</volume><number>5473</number><keywords><keyword>t etrahymena-thermophila ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>activesite</keyword><keyword>substrate</keyword><keyword>binding</keyword><keyw ord>dynamics</keyword><keyword>titin</keyword><keyword>pathways</keyword> <keyword>protein</keyword><keyword>steps</keyword></keywords><dates><year >2000</year><pub-dates><date>Jun 16</date></pub-dates></dates><isbn>00368075</isbn><accession-num>ISI:000087687000052</accessionnum><urls><related-urls><url><Go to ISI>://000087687000052</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Rus sell</Author><Year>2002</Year><RecNum>11</RecNum><record><recnumber>11</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Russell, R.</author><author>Zhuang, X. W.</author><author>Babcock, H. P.</author><author>Millett, I. S.</author><author>Doniach, S.</author><author>Chu, S.</author><author>Herschlag, D.</author></authors></contributors><authaddress>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Stanford, CA 94305 USA
Stanford Univ, Dept Chem, Stanford, CA 94305 USA
Stanford Univ, Dept Appl Phys, Stanford, CA 94305 USA</auth-address><titles><title>Exploring the folding landscape of a structured RNA</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>155160</pages><volume>99</volume><number>1</number><keywords><keyword>selfsplicing rna</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>catalytic rna</keyword><keyword>secondary structure</keyword><keyword>energy landscape</keyword><keyword>escherichia-coli</keyword><keyword>ribosomalrna</keyword><keyword>kinetic traps</keyword><keyword>pathways</keyword><keyword>molecule</keyword></ke ywords><dates><year>2002</year><pub-dates><date>Jan 8</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000173233300031</accession-num><urls><related-urls><url><Go to ISI>://000173233300031</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Zhu ang</Author><Year>2000</Year><RecNum>10</RecNum><record><recnumber>10</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Zhuang, X. W.</author><author>Bartley, L. E.</author><author>Babcock, H. P.</author><author>Russell, R.</author><author>Ha, T. J.</author><author>Herschlag, D.</author><author>Chu, S.</author></authors></contributors><auth-address>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Beckman Ctr B400, Stanford, CA 94305 USA</auth-address><titles><title>A single-molecule study of RNA catalysis and folding</title><secondarytitle>Science</secondary-title></titles><pages>20482051</pages><volume>288</volume><number>5473</number><keywords><keyword>t etrahymena-thermophila ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>activesite</keyword><keyword>substrate</keyword><keyword>binding</keyword><keyw ord>dynamics</keyword><keyword>titin</keyword><keyword>pathways</keyword> <keyword>protein</keyword><keyword>steps</keyword></keywords><dates><year >2000</year><pub-dates><date>Jun 16</date></pub-dates></dates><isbn>00368075</isbn><accession-num>ISI:000087687000052</accessionnum><urls><related-urls><url><Go to ISI>://000087687000052</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (9, 22, 23) . RNA Conformational Change: Electrostatic Relaxation versus BarrierCrossing Process Electrostatic compaction into a nonspecifically collapsed structure has been shown by time-resolved SAXS to occur in < 100 msec (15). When EFRET states at low and high [Mg2+] are grouped together (Table 1) according to electrostatic relaxation connectivity, the EFRET values in each group show a monotonic increase with [Mg2+], consistent with a progressively more collapsed RNA structure at higher [Mg2+] due to better electrostatic screening of the RNA phosphate backbone. This EFRET shift with [Mg2+] is also observed in the EFRET histograms in the equilibrium FRET measurements of the same RNA ADDIN EN.CITE <EndNote><Cite><Author>Smith</Author><Year>2007</Year><RecNum>14</RecNum> <record><rec-number>14</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Smith, G., Lee, K.T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite></EndNote> (8) , although in that case the relationship between EFRET states cannot be directly observed. For the [Mg2+] intervals with only two EFRET states populated, the EFRET states are referred to as low and high EFRET states. For simplicity, [Mg2+] intervals with multiple EFRET states, group numbers (I-IV) instead of the specific EFRET values are used to refer to the EFRET states (see Table 1 and Fig. 4). The transitions between EFRET states from different electrostatically-related groups (see Table 1 and Fig. 4) are barriercrossing processes that occur during the constant [Mg2+] intervals, while the transitions between EFRET states from the same group are electrostatic relaxation processes observed only during the ~1sec [Mg2+]transition time. An exception is the conformational change between states I and II for the [Mg2+ j d ( [ c t u u i M r h m r . g o e p i e 2 s T F 0 T F 0 t h k o 0 a c e w o . h i . w i i f . r o x o l 0 e g 0 o s n - S t a d i n g 1 ”!1 . s i n . 3 1 ”!1 . - s t a t o g r e t i c t h e 1 ”!0 . n o t t r a s i b i t 0 e n h c o n n g t . b a + ] - t s i n g e l e c d h r r i e r a h t r t e f 0 m g l A 0 m t e a m s u n 1 m s t , c t i c i e n s a p o s o o r i p t n , n s t c r t i o e n i a t i U n f o o r [ M M e - m o l s h o w M j u m u n f o s a n d a r e v f o l d i M j u s h o w n b o t h o m p l i w a o n n c h i c n t s s i t i g c r e h [ n m o l ] = h M g g ) e n c a x 0 . 0 a p p 2 + ] a n ( i . u r r a t i 1 ”!1 e n s i n d d e . e n t o n ) . 0 b t e u r b a l y . m o r i r M t v n r w h a l g i e r i t h l d i n g a n d M u l t i - S t a t e g 2 + ] = 0 . 0 1 ”!0 . 4 a n d e c u l e t h a t p e x p l d i n g p o p u e r y s n g i n t d e s f o r b j u m p c a t e d t e . l i t c r t r a h e r i m E F a t i m i l e r v r i b e v i c o n m u l j 0 e R o a a e t d t e . n E n r l d y i i c t o r i 0 1 ”!0 . t s e x T r e l a t o t f o r , a n d . I n t i o n s - s t a t e s o f 4 a n d h i b i t x a t i o n h o s e t h u s e f f 0 e [ < o l d i n g ( F i g . 3 ) . M u l t i - s t a t e o l d i n g i s u n e x p e c t e d f o r t h e . 0 1 ”!0 . 4 m M j u m p e x p e r i m e n t b e c a u s e q u i l i b r i u m m e a s u r e m e n t s f o r M g 2 + ] d"0 . 4 m M A D D I N E N . C I T E E n d N o t e > < C i t e > < A u t h o r > S m i t h < / A u t h o r > < Y e a r > 2 0 0 7 < / Y e a r > < R e c N u m > 1 4 < / R e c N u m > < r e c o r d > < r e c - n u m b e r > 1 4 < / r e c n u m b e r > < r e f - t y p e n a m e = " J o u r n a l A r t i c l e " > 1 7 < / r e f t y p e > < c o n t r i b u t o r s > < a u t h o r s > < a u t h o r > S m i t h , G . , L e e , K.-T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite></EndNote> (8) show only two-state trajectories for the majority of single molecules. This dramatic deviation from equilibrium behavior is a first indication that the periodic jump technique is able to probe regions of the free energy surface that are virtually unsampled at equilibrium. EFRET histograms (Fig. 3-B1, B3) and trajectories show that RNA molecules folding from the high EFRET state (IV) always go to the highest EFRET state (state IV) with only very infrequent transitions to state III* (Fig. 4). On the other hand, molecules folding from the low EFRET state (I) evolve to populate four EFRET states (Fig. 3-B2,B4, Table 1), some of which are intermediate states not observed in equilibrium measurements (Fig. 3-B insets). The folding kinetics for the two jump conditions will be discussed separately below. During the [Mg2+] = 0.4mM folding interval (Fig. 3-C1), RNA molecules that fold from state I primarily go to state II within 3 sec, and the subsequent population relaxation is predominantly to state III. There is also a slow but steady increase in the population of state IV within the 10-sec interval consistent with the expectation from our equilibrium measurements (Fig. 3-B2 inset). States II and III are thus intermediates along the folding pathway with state II preceding state III. Since the populations of EFRET states II and III decrease with increasing period of the perturbation (data not shown), one should also allow that these intermediates are sampling conformations in what would be the transition state region at equilibrium. F o l d i n g u n d e r t h e 0 . 0 1 ”!1 . 0 m M j u m p c o n d i t i o n ( F i g . 3 C 2 ) i s s i m i l a r , a n d m o l e c u l e s i n i t i a l l y i n s t a t e I a g a i n s t r o n g l y f a v o r g o i n g t o s t a t e I I . T h e t r a n s i t i o n i s f a s t , c o m p l e t e w i t h i n t h e ~ 1 s [ M g 2 + ] - c h a n g e . F r o m s t a t e I I , R N A m o l e c u l e s s h i f t p o p u l a t i o n t o s t ate III, which continues to accumulate within the 10 second interval. The difference between folding at 0.4mM and folding at 1mM is that the native state is thermodynamically stable and populated at equilibrium at 1mM. The native state is characterized by an EFRET value of 0.45 ADDIN EN.CITE <EndNote><Cite><Author>Smith</Author><Year>2007</Year><RecNum>14</RecNum> <record><rec-number>14</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Smith, G., Lee, K.T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite></EndNote> (8) , indistinguishable from the EFRET value of state II (Fig. 3-B4 inset), suggesting similarity in conformation (or distance between dye molecules) for these two states as probed by FRET. However, state II is not monotonically populated in the folding interval, as would be expected for the native state. This contradiction is strong evidence that state II is not identical to the native state, and that these two states differ in some hidden DOF. We conclude that the observed axis responds rapidly to the [Mg2+] change while a hidden DOF relaxes more slowly. Much longer time ( EMBED Equation.DSMT4 10sec) is required for both the observed axis and the hidden DOF to relax to the native state. Variation of [Mg2+] period To further establish the sensitivity to hidden DOFs and non-Markovian dynamics, we varied the period of the perturbation. Figure 5 shows a comparison of the low EFRET, low [Mg2+] sub-ensemble results for 20 sec and 10 sec periods (i.e. 10 sec vs. 5 sec [Mg2+] intervals). If the dynamics were of a 2-state Markovian process one would expect the relaxation (kinetics) to be the same. However, the shorter period data relax much faster. In the longer high [Mg2+] interval the RNA molecules are driven further from the low [Mg2+] steady state (almost equilibrium) position in the longer high [Mg2+] interval. Since the observed DOF then has more time to “couple” with the hidden DOF, the dynamics of the observed DOF become slower (or more non-Markovian). In the language of this paper, the more the molecule folds in the high [Mg2+] interval the more difficult it is to unfold in the low [Mg2+] interval. Discussion Folding at High [Mg2+] is Slow and Multi-State , Unfolding at Low [Mg2+] is Fast and Two-State For the unfolding interval, all three jump experiments exhibit two-state kinetics, and the population distributions at the end of the 10-sec interval are close to the equilibrium result (Fig. 2-C1, C2, unfolding intervals for the 0.01(0.4 and 0.01 (1 mM Mg2+ are not shown for brevity). This population shift indicates that at low [Mg2+], relaxation appears to be nearly complete within the 10-sec interval regardless of the initial EFRET state or original high [Mg2+]. Folding, on the other hand, is more complicated; multiple intermediate states are involved and events originating from the low or high EFRET states behave very differently. The EFRET population distributions at the end of the high [Mg2+] interval for all three jump conditions (Figs. 2-C3, C4 and 3-C) are far from their equilibrium distributions. Thus, the RNA population does not achieve equilibrium in the 10-sec high [Mg2+] interval. This is consistent with previous observations that folding is slower and more complicated than unfolding ADDIN EN.CITE <EndNote><Cite><Author>Russell</Author><Year>2002</Year><RecNum>11</RecNu m><record><rec-number>11</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Russell, R.</author><author>Zhuang, X. W.</author><author>Babcock, H. P.</author><author>Millett, I. S.</author><author>Doniach, S.</author><author>Chu, S.</author><author>Herschlag, D.</author></authors></contributors><auth-address>Herschlag, D
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Phys, Stanford, CA 94305 USA
Stanford Univ, Dept Biochem, Stanford, CA 94305 USA
Stanford Univ, Dept Chem, Stanford, CA 94305 USA
Stanford Univ, Dept Appl Phys, Stanford, CA 94305 USA</authaddress><titles><title>Exploring the folding landscape of a structured RNA</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>155160</pages><volume>99</volume><number>1</number><keywords><keyword>selfsplicing rna</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>catalytic rna</keyword><keyword>secondary structure</keyword><keyword>energy landscape</keyword><keyword>escherichia-coli</keyword><keyword>ribosomalrna</keyword><keyword>kinetic traps</keyword><keyword>pathways</keyword><keyword>molecule</keyword></ke ywords><dates><year>2002</year><pub-dates><date>Jan 8</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000173233300031</accession-num><urls><related-urls><url><Go to ISI>://000173233300031</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (9) ; unfolding involves a spontaneous and complete opening of the RNA structure, while folding is entropically unfavorable, requiring structural elements to assemble in the correct order. Hidden Degrees of Freedom and Long Memory Effect The crystal structure of RNase P RNA ADDIN EN.CITE <EndNote><Cite><Author>Kazantsev</Author><Year>2005</Year><RecNum>35</Rec Num><record><rec-number>35</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kazantsev, A. V.</author><author>Krivenko, A. A.</author><author>Harrington, D. J.</author><author>Holbrook, S. R.</author><author>Adams, P. D.</author><author>Pace, N. R.</author></authors></contributors><authaddress>Pace, NR
Univ Colorado, Dept Mol Cellular & Dev Biol, Boulder, CO 80309 USA
Univ Colorado, Dept Mol Cellular & Dev Biol, Boulder, CO 80309 USA
Stanford Univ, Stanford Synchrotron Radiat Lab, Menlo Pk, CA 94025 USA
Univ Calif Berkeley, Lawrence Berkeley Lab, Phys Biosci Div, Berkeley, CA 94720 USA
Univ Calif Berkeley, Lawrence Berkeley Lab, Computat Crystallog Initiat, Berkeley, CA 94720 USA</auth-address><titles><title>Crystal structure of a bacterial ribonuclease P RNA</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary- title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>1339213397</pages><volume>102</volume><number>38</number><keywords><keyword>ri bozyme</keyword><keyword>rna crystallography</keyword><keyword>trna processing</keyword><keyword>metal-ion binding</keyword><keyword>large ribosomal-subunit</keyword><keyword>pre-transferrna</keyword><keyword>bacillus-subtilis</keyword><keyword>activesite</keyword><keyword>tertiary interaction</keyword><keyword>angstrom resolution</keyword><keyword>escherichiacoli</keyword><keyword>magnesium-ions</keyword><keyword>precursor trna(asp)</keyword></keywords><dates><year>2005</year><pubdates><date>Sep 20</date></pub-dates></dates><isbn>00278424</isbn><accession-num>ISI:000232115100009</accessionnum><urls><related-urls><url><Go to ISI>://000232115100009</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (30) suggests that the positions labeled with the FRET dyes (3’ end and L18 loop) are not directly involved in the formation of the core structure. However, it is reasonable to expect that the observed (i.e. labeled) DOF will report on the structure and dynamics of the unlabeled parts of the RNA due to structural connectivity ADDIN EN.CITE <EndNote><Cite><Author>Smith</Author><Year>2007</Year><RecNum>14</RecNum> <record><rec-number>14</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Smith, G., Lee, K.T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F.</author></authors></contributors><titles><title>Single Molecule measurements reveal the deeply fluted free energy surface of a large RNA in collapsed state</title><secondary-title>submitted to J. Mol. Biol</secondary-title></titles><periodical><full-title>submitted to J. Mol. Biol</fulltitle></periodical><dates><year>2007</year></dates><urls></urls></record> </Cite></EndNote> (8) . All three jump experiments reported here indicate that the structural changes of the unlabeled parts affect the observed dynamics of the labeled axis but not the EFRET values. Folding at [Mg2+] = 0.1mM is characterized by two kinetically distinct high EFRET states: molecules that fold from an initial high EFRET state end up in a stable long-lived high EFRET state, while molecules that fold from the low EFRET state fluctuate quite actively between low and high EFRET states. These two behaviors result from conformational differences in the hidden DOFs. Folding at [Mg2+] = 1mM includes transient population of a EFRET state (state II) with the same EFRET value as the native state, but which behaves as a kinetic intermediate. Further structural changes in a hidden DOF that require >> 10 sec are required to achieve the true native state. Slow dynamics in the hidden DOFs give rise to long memory effects in the single-molecule EFRET trajectories. Figure S4 shows two RNA molecules that retain dramatically different dynamics in the observed FRET DOF for several minutes; some molecules remain in the low or high EFRET states (Figs. S4-a,b) while other molecules synchronize with the periodic [Mg2+]-jumps and switch between low and high EFRET states (Fig. S4-c). Persistent behavior is likely to result from structural/conformational differences in some hidden DOF. Stabilizing Effects of Mg2+ on RNA Structure and Cooperative RNA Folding Mg2+ ions stabilize RNA structure by allowing tertiary contacts to form through specific ion binding, and by electrostatically screening the phosphate backbone ADDIN EN.CITE <EndNote><Cite><Author>Draper</Author><Year>2005</Year><RecNum>24</RecNum ><record><rec-number>24</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Draper, D. E.</author><author>Grilley, D.</author><author>Soto, A. M.</author></authors></contributors><auth-address>Draper, DE
Johns Hopkins Univ, Dept Chem, Charles & 34Th St, Baltimore, MD 21218 USA
Johns Hopkins Univ, Dept Chem, Baltimore, MD 21218 USA
Johns Hopkins Univ, Program Mol & Computat Biophys, Baltimore, MD 21218 USA</auth-address><titles><title>Ions and RNA folding</title><secondarytitle>Annual Review of Biophysics and Biomolecular Structure</secondarytitle></titles><periodical><full-title>Annual Review of Biophysics and Biomolecular Structure</full-title><abbr-1>Annu. Rev. Biophys. Biomol. Struct.</abbr-1><abbr-2>Annu Rev Biophys Biomol Struct</abbr2></periodical><pages>221243</pages><volume>34</volume><keywords><keyword>magnesium</keyword><keyw ord>potassium</keyword><keyword>electrostatics</keyword><keyword>poissonboltzmann theory</keyword><keyword>hydration</keyword><keyword>phenylalanine transfer-rna</keyword><keyword>molecular-dynamics simulations</keyword><keyword>dimerization initiation site</keyword><keyword>x-ray-scattering</keyword><keyword>group-i intron</keyword><keyword>metal-ions</keyword><keyword>crystalstructure</keyword><keyword>nucleic-acids</keyword><keyword>tertiary structure</keyword><keyword>ribosomalrna</keyword></keywords><dates><year>2005</year></dates><isbn>10568700</isbn><accession-num>ISI:000230099600010</accessionnum><urls><related-urls><url><Go to ISI>://000230099600010</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (3) . For all three jump conditions, the RNA molecules were observed to become compact upon [Mg2+] increase (Fig. 4). This compaction is mainly due to the nonspecific electrostatic relaxation of the RNA structure, but it has been shown for other RNA molecules that some tertiary interactions might also be formed during the electrostatic relaxation process ADDIN EN.CITE <EndNote><Cite><Author>Woodson</Author><Year>2005</Year><RecNum>36</RecNu m><record><rec-number>36</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Woodson, S. A.</author></authors></contributors><auth-address>Woodson, SA
Johns Hopkins Univ, TC Jenkins Dept Biophys, 3400 N Charles St, Baltimore, MD 21218 USA
Johns Hopkins Univ, TC Jenkins Dept Biophys, Baltimore, MD 21218 USA</auth-address><titles><title>Metal ions and RNA folding: a highly charged topic with a dynamic future</title><secondarytitle>Current Opinion in Chemical Biology</secondarytitle></titles><periodical><full-title>Current Opinion in Chemical Biology</full-title><abbr-1>Curr. Opin. Chem. Biol.</abbr-1><abbr-2>Curr Opin Chem Biol</abbr-2></periodical><pages>104109</pages><volume>9</volume><number>2</number><keywords><keyword>delta virus ribozyme</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>group-i ribozyme</keyword><keyword>conformational switch</keyword><keyword>electrostatic properties</keyword><keyword>counterion condensation</keyword><keyword>thermodynamic framework</keyword><keyword>poisson-boltzmann</keyword><keyword>crystalstructure</keyword><keyword>nucleicacids</keyword></keywords><dates><year>2005</year><pubdates><date>Apr</date></pub-dates></dates><isbn>13675931</isbn><accession-num>ISI:000228607700003</accessionnum><urls><related-urls><url><Go to ISI>://000228607700003</url></relatedurls></urls><language>English</language></record></Cite><Cite><Author>Kwo k</Author><Year>2006</Year><RecNum>50</RecNum><record><recnumber>50</rec-number><ref-type name="Journal Article">17</reftype><contributors><authors><author>Kwok, L. W.</author><author>Shcherbakova, I.</author><author>Lamb, J. S.</author><author>Park, H. Y.</author><author>Andresen, K.</author><author>Smith, H.</author><author>Brenowitz, M.</author><author>Pollack, L.</author></authors></contributors><authaddress>Pollack, L
Cornell Univ, Sch Appl & Engn Phys, Ithaca, NY 14853 USA
Cornell Univ, Sch Appl & Engn Phys, Ithaca, NY 14853 USA
Yeshiva Univ Albert Einstein Coll Med, Dept Biochem, Bronx, NY 10461 USA
Yeshiva Univ Albert Einstein Coll Med, Ctr Synchrotron Biosci, Bronx, NY 10461 USA</auth-address><titles><title>Concordant exploration of the kinetics of RNA folding from global and local perspectives</title><secondary-title>Journal of Molecular Biology</secondary-title></titles><periodical><full-title>Journal of Molecular Biology</full-title><abbr-1>J. Mol. Biol.</abbr-1><abbr-2>J Mol Biol</abbr-2></periodical><pages>282293</pages><volume>355</volume><number>2</number><keywords><keyword>rna folding</keyword><keyword>time-resolved small-angle x-ray scattering</keyword><keyword>electrostatic relaxation</keyword><keyword>compaction</keyword><keyword>tertiary structure formation</keyword><keyword>tetrahymena-thermophila ribozyme</keyword><keyword>x-ray-scattering</keyword><keyword>group-i ribozyme</keyword><keyword>monovalent cations</keyword><keyword>peripheral element</keyword><keyword>pathways</keyword><keyword>domain</keyword><key word>compaction</keyword><keyword>events</keyword><keyword>p5abc</keyword ></keywords><dates><year>2006</year><pub-dates><date>Jan 13</date></pubdates></dates><isbn>0022-2836</isbn><accessionnum>ISI:000234371900011</accession-num><urls><related-urls><url><Go to ISI>://000234371900011</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (4, 28) . Achieving high cooperativity in folding ADDIN EN.CITE <EndNote><Cite><Author>Fang</Author><Year>2003</Year><RecNum>32</RecNum>< record><rec-number>32</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, X. W.</author><author>Srividya, N.</author><author>Golden, B. L.</author><author>Sosnick, T. R.</author><author>Pan, T.</author></authors></contributors><auth-address>Sosnick, TR
Univ Chicago, Dept Biochem & Mol Biol, 920 E 58th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Purdue Univ, Dept Biochem, W Lafayette, IN 47907 USA
Univ Chicago, Inst Biophys Dynam, Chicago, IL 60637 USA</auth- address><titles><title>Stepwise conversion of a mesophilic to a thermophilic ribozyme</title><secondary-title>Journal of Molecular Biology</secondary-title></titles><periodical><full-title>Journal of Molecular Biology</full-title><abbr-1>J. Mol. Biol.</abbr-1><abbr-2>J Mol Biol</abbr-2></periodical><pages>177183</pages><volume>330</volume><number>2</number><keywords><keyword>riboz yme</keyword><keyword>folding</keyword><keyword>stability</keyword><keywo rd>cooperativity</keyword><keyword>thermophile</keyword><keyword>ribonucl ease-p rna</keyword><keyword>secondary</keyword><keyword>stability</keyword></ke ywords><dates><year>2003</year><pub-dates><date>Jul 4</date></pubdates></dates><isbn>0022-2836</isbn><accessionnum>ISI:000183824900001</accession-num><urls><related-urls><url><Go to ISI>://000183824900001</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (31) ADDIN EN.CITE <EndNote><Cite><Author>Fang</Author><Year>2001</Year><RecNum>37</RecNum>< record><rec-number>37</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, X. W.</author><author>Golden, B. L.</author><author>Littrell, K.</author><author>Shelton, V.</author><author>Thiyagarajan, P.</author><author>Pan, T.</author><author>Sosnick, T. R.</author></authors></contributors><auth-address>Sosnick, TR
Univ Chicago, Dept Biochem & Mol Biol, 920 E 58Th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Purdue Univ, Dept Biochem, W Lafayette, IN 47907 USA
Argonne Natl Lab, Argonne, IL 60439 USA
Univ Chicago, Dept Chem, Chicago, IL 60637 USA
Univ Chicago, Inst Biophys Dynam, Chicago, IL 60637 USA</auth-address><titles><title>The thermodynamic origin of the stability of a thermophilic ribozyme</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</fulltitle><abbr-1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>43554360</pages><volume>98</volume><number>8</number><keywords><keyword>subti lis rnase-p</keyword><keyword>small-angle scattering</keyword><keyword>crystalstructure</keyword><keyword>ribonuclease-p</keyword><keyword>angstrom resolution</keyword><keyword>substratebinding</keyword><keyword>domain</keyword><keyword>temperature</keyword>< keyword>secondary</keyword><keyword>perspective</keyword></keywords><date s><year>2001</year><pub-dates><date>Apr 10</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000168059700020</accession-num><urls><related-urls><url><Go to ISI>://000168059700020</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (27) requires some preorganization of the structure. Topological constraints of the native state requires sequential formation of the following helices: P4 first, then P2, then finally P5, with a number of noncanonical stabilizing interactions. Formation of these helices in different order or combinations may result in intermediate states that are kinetically stable. No ensemble kinetic experiments have been reported for the Cthermo thermophilic ribozyme. However, a rate limiting step along the folding pathway of a mesophilic homologue has been kinetically characterized in the ensemble. A folding intermediate was directly observed ADDIN EN.CITE <EndNote><Cite><Author>Fang</Author><Year>2002</Year><RecNum>42</RecNum>< record><rec-number>42</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, X. W.</author><author>Thiyagarajan, P.</author><author>Sosnick, T. R.</author><author>Pan, T.</author></authors></contributors><authaddress>Sosnick, TR
Univ Chicago, Dept Biochem & Mol Biol, 920 E 58Th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Argonne Natl Lab, Argonne, IL 60439 USA
Univ Chicago, Inst Biophys Dynam, Chicago, IL 60637 USA</authaddress><titles><title>The rate-limiting step in the folding of a large ribozyme without kinetic traps</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>85188523</pages><volume>99</volume><number>13</number><keywords><keyword>phen ylalanine transfer-rna</keyword><keyword>tetrahymena ribozyme</keyword><keyword>crystal-structure</keyword><keyword>angstrom resolution</keyword><keyword>p rna</keyword><keyword>domain</keyword><keyword>pathway</keyword><keyword> binding</keyword><keyword>core</keyword><keyword>mg2+</keyword></keywords ><dates><year>2002</year><pub-dates><date>Jun 25</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000176478200013</accession-num><urls><related-urls><url><Go to ISI>://000176478200013</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (26) , and an unfolding intermediate was deduced from a [Mg2+]-chevron analysis ADDIN EN.CITE <EndNote><Cite><Author>Fang</Author><Year>1999</Year><RecNum>47</RecNum>< record><rec-number>47</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, X. W.</author><author>Pan, T.</author><author>Sosnick, T. R.</author></authors></contributors><auth-address>Pan, T
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA</authaddress><titles><title>Mg2+-dependent folding of a large ribozyme without kinetic traps</title><secondary-title>Nature Structural Biology</secondary-title></titles><periodical><full-title>Nature Structural Biology</full-title><abbr-1>Nature Struct. Biol.</abbr1><abbr-2>Nature Struct Biol</abbr-2></periodical><pages>10911095</pages><volume>6</volume><number>12</number><keywords><keyword>group -i ribozyme</keyword><keyword>rnasep</keyword><keyword>proteins</keyword></keywords><dates><year>1999</year> <pub-dates><date>Dec</date></pub-dates></dates><isbn>10728368</isbn><accession-num>ISI:000084022300007</accessionnum><urls><related-urls><url><Go to ISI>://000084022300007</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (14) . The rate-limiting step to the native state was described as a small- amplitude conformational change (i.e. no change in radius of gyration or burial of surface area) between these two intermediate states ADDIN EN.CITE <EndNote><Cite><Author>Fang</Author><Year>2002</Year><RecNum>42</RecNum>< record><rec-number>42</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, X. W.</author><author>Thiyagarajan, P.</author><author>Sosnick, T. R.</author><author>Pan, T.</author></authors></contributors><authaddress>Sosnick, TR
Univ Chicago, Dept Biochem & Mol Biol, 920 E 58Th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Argonne Natl Lab, Argonne, IL 60439 USA
Univ Chicago, Inst Biophys Dynam, Chicago, IL 60637 USA</authaddress><titles><title>The rate-limiting step in the folding of a large ribozyme without kinetic traps</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>85188523</pages><volume>99</volume><number>13</number><keywords><keyword>phen ylalanine transfer-rna</keyword><keyword>tetrahymena ribozyme</keyword><keyword>crystal-structure</keyword><keyword>angstrom resolution</keyword><keyword>p rna</keyword><keyword>domain</keyword><keyword>pathway</keyword><keyword> binding</keyword><keyword>core</keyword><keyword>mg2+</keyword></keywords ><dates><year>2002</year><pub-dates><date>Jun 25</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000176478200013</accession-num><urls><related-urls><url><Go to ISI>://000176478200013</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (26) . No additional Mg2+ ions are bound in this step, which argues for a local consolidation of RNA structure around a prebound Mg2+ ion. This lack of change in global structural dimensions is consistent with the indistinguishable EFRET values of states III and III* and would allow these states to lie on either side of the major barrier (Fig. 1-B). However, further experiments are reuired to prove that our hidden DOF is the major barrier to folding. In the mesophilic homologue, the folding rate at high [Mg2+] is more than one order of magnitude slower than the unfolding rate at very low cation concentration ADDIN EN.CITE <EndNote><Cite><Author>Fang</Author><Year>2002</Year><RecNum>42</RecNum>< record><rec-number>42</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, X. W.</author><author>Thiyagarajan, P.</author><author>Sosnick, T. R.</author><author>Pan, T.</author></authors></contributors><authaddress>Sosnick, TR
Univ Chicago, Dept Biochem & Mol Biol, 920 E 58Th St, Chicago, IL 60637 USA
Univ Chicago, Dept Biochem & Mol Biol, Chicago, IL 60637 USA
Argonne Natl Lab, Argonne, IL 60439 USA
Univ Chicago, Inst Biophys Dynam, Chicago, IL 60637 USA</authaddress><titles><title>The rate-limiting step in the folding of a large ribozyme without kinetic traps</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr- 1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>85188523</pages><volume>99</volume><number>13</number><keywords><keyword>phen ylalanine transfer-rna</keyword><keyword>tetrahymena ribozyme</keyword><keyword>crystal-structure</keyword><keyword>angstrom resolution</keyword><keyword>p rna</keyword><keyword>domain</keyword><keyword>pathway</keyword><keyword> binding</keyword><keyword>core</keyword><keyword>mg2+</keyword></keywords ><dates><year>2002</year><pub-dates><date>Jun 25</date></pubdates></dates><isbn>0027-8424</isbn><accessionnum>ISI:000176478200013</accession-num><urls><related-urls><url><Go to ISI>://000176478200013</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (26) . This is qualitatively consistent with our observation that for all three jump conditions unfolding is largely complete within the 10-sec low [Mg2+] interval while folding is far from equilibrium within the 10-sec high [Mg2+] interval (Figs. 2-C, 3-C). Thus our conclusion of the existence of high barriers in the [Mg2+] jump experiments of CthermoL18 RNA qualitatively agrees with the ensemble kinetic measurements of the mesophilic homologue. Free Energy Landscape The connectivity of the EFRET states along the folding pathway (Figs. 2C, 3-C, 4) and the rate constants for interconversion between two connected EFRET states (Table S1) are readily obtained from the singlemolecule RNA response to [Mg2+]-jumps monitored over time. Although each jump experiment differs in detail (e.g., the barrier heights and number of free energy basins), a qualitative free energy landscape with the major features of all three jump experiments can be illustrated as in Fig. 1-B. A [Mg2+] change causes the free energy landscape to shift with subsequent RNA population redistribution towards equilibrium on the new free energy landscape. Molecules take one of two alternative folding pathways depending on which EFRET state (low (I) or high (II)) a molecule occupies prior to the [Mg2+]-jump. The two folding pathways are separated by a high barrier that correspon d s t o a s t r u c t u r a l c h a n g e i n s o m e h i d d e n D O F . T h i s b a r r i e r i s s o h i g h t h a t t r a n s i t i o n s o v e r i t a r e o n l y r a r e l y o b s e r v e d . F o r t h e 0 . 0 1 ”!0 . 4 m M a n d 0 . 0 1 ”!1 . 0 m M j u m p c o n d i t i o n s , t h e E F R E T h i s t o g r a m s ( F i g . 3 - B ) , c o n n e c t i v i t y o f t h e E F R E T s t a t e s ( F i g . 4 ) , a n d ( r a re) observation of transitions over the barrier (Fig. 3-A2 lower trajectory, arrow) allow assignment of the barrier between states III and III*; they posses the same observed EFRET value but are kinetically distinct and therefore on the opposite sides of the barrier. Probing regions of the free energy landscape that are inaccessible to equilibrium results In contrast to perturbation experiments with only a single jump, the period of the periodic jump experiment can be used to probe macromolecular free energy landscapes. When the period of [Mg2+]-jumps is shorter than the timescale for relaxation, the distribution of RNA conformations at the end of an interval will not have reached equilibrium. The response of this non-equilibrium distribution of starting conformations to the next [Mg2+]-jump will depend on how far the system is from each of the two asymptotic equilibrium distributions. The system’s “distance” from equilibrium is controlled by the length of the periodic [Mg2+] jumps. Fig. 5 shows that the ribozyme is perturbed less during the 5 second interval (vs. 10 sec interval), and so it relaxes more quickly. If one assumes linear response (but near equilibrium) then the relaxation rate should be independent of perturbation. The observed dependence of relaxation kinetics on the length of [Mg2+] jump period is evidence that a non-linear (or non-Markovian) response describes the RNA dynamics in this experiment. Additionally, the RNA populations driven for different periods cannot be equilibrating to the same distributions of states. Therefore, different regions of the free energy surface are probed with different period lengths. The result of the period-dependence is a direct manifestation of memory in the dynamics. With a long enough sequence of periodic jump cycles, the molecules are best described by a non-equilibrium steady state distribution of conformations ADDIN EN.CITE <EndNote><Cite><Author>Tietz</Author><Year>2006</Year><RecNum>54</RecNum> <record><rec-number>54</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Tietz, C.</author><author>Schuler, S.</author><author>Speck, T.</author><author>Seifert, U.</author><author>Wrachtrup, J.</author></authors></contributors><auth-address>Tietz, C
Univ Stuttgart, Inst Phys 3, D-70550 Stuttgart, Germany
Univ Stuttgart, Inst Phys 3, D-70550 Stuttgart, Germany
Univ Stuttgart, Inst Theoret Phys 2, D-70550 Stuttgart, Germany</authaddress><titles><title>Measurement of stochastic entropy production</title><secondary-title>Physical Review Letters</secondarytitle></titles><periodical><full-title>Physical Review Letters</fulltitle><abbr-1>Phys. Rev. Lett.</abbr-1><abbr-2>Phys Rev Lett</abbr2></periodical><pages>050602</pages><volume>97</volume><number>5</number> <keywords><keyword>free-energy differences</keyword><keyword>fluctuation theorem</keyword><keyword>steadystates</keyword><keyword>equality</keyword><keyword>dynamics</keyword></k eywords><dates><year>2006</year><pub-dates><date>Aug 4</date></pubdates></dates><isbn>0031-9007</isbn><accessionnum>ISI:000239520300011</accession-num><urls><related-urls><url><Go to ISI>://000239520300011</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (32) . In one limit for a 2-state system, what appear to be new intermediates may actually be conformations that are those of the transition state separating two basins at equilibrium (note state II in Figure 3C1). Conclusions We developed and applied a single-molecule periodic [Mg2+]-jump method, to study the Mg2+-induced folding of CthermoL18 RNA. The observed connectivity of EFRET states and the associated rate constants allow construction of a detailed free energy landscape. We find that molecules starting from the two different interconverting conformations (i.e. the low and high EFRET states) before a [Mg2+] increase traverse two distinct regions of the landscape, which are separated by a very high free energy barrier. This rate limiting step involves only changes in the hidden DOF and does not induce detectable change in the EFRET value. The slow dynamics, apparent in the hidden DOF, give rise to more details of the free energy landscape and clearly reveal long memory effects in the single-molecule EFRET trajectories. The fact that the relaxation dynamics depend on the magnitude (duration) of the perturbation for a fixed [Mg2+] clearly indicates that the response is non-Markovian as is expected for a non-equilibrium steady state system with long memory. Many important RNA folding questions can be studied with this approach, such as the origin and properties of long memory effects, and cooperative folding of large RNAs at high [Mg2+]. Quantitative modeling of the observed dynamics, such as a Generalized Langevin Equation simulation with a memory kernel ADDIN EN.CITE <EndNote><Cite><Author>Min</Author><Year>2006</Year><RecNum>55</RecNum><r ecord><rec-number>55</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Min, W.</author><author>Xie, X. S.</author></authors></contributors><authaddress>Xie, XS
Harvard Univ, Dept Chem & Chem Biol, Cambridge, MA 02138 USA
Harvard Univ, Dept Chem & Chem Biol, Cambridge, MA 02138 USA</auth-address><titles><title>Kramers model with a power-law friction kernel: Dispersed kinetics and dynamic disorder of biochemical reactions</title><secondary-title>Physical Review E</secondarytitle></titles><periodical><full-title>Physical Review E</fulltitle></periodical><pages>010902(R)</pages><volume>73</volume><number>1</ number><keywords><keyword>single-molecule kinetics</keyword><keyword>chemical-reactions</keyword><keyword>enzymatic dynamics</keyword><keyword>brownian dynamics</keyword><keyword>relaxation</keyword><keyword>bottleneck</keywo rd><keyword>proteins</keyword><keyword>escape</keyword><keyword>decay</ke yword></keywords><dates><year>2006</year><pubdates><date>Jan</date></pub-dates></dates><isbn>15393755</isbn><accession-num>ISI:000235008500008</accessionnum><urls><related-urls><url><Go to ISI>://000235008500008</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (33) , will provide more insights into RNA folding mechanisms. Finally, measurements with a set of different [Mg2+]-jump periods will allow construction of a more comprehensive free energy landscape which is inaccessible from equilibrium measurements and traditional single-jump techniques. Materials and Methods Details of data acquisition and analysis are described in the Supplementary Material. Acknowledgements We thank the Ismagilov group, especially Helen Song, for help with making PDMS devices and discussions about microfluidic systems. This work was supported by National Institutes of Health (GM067961), and the Burroughs Wellcome Fund Interfaces ID 1001774 with a fellowship to XQ. NFS thanks the John S. Guggenheim Foundation for a fellowship. References: ADDIN EN.REFLIST 1. Alberts, B. (2002) Molecular biology of the cell (Garland Science, New York). 2. Lilley, D. M. J. (2005) Current Opinion in Structural Biology 15, 313-323. 3. Draper, D. E., Grilley, D. & Soto, A. M. (2005) Annual Review of Biophysics and Biomolecular Structure 34, 221-243. 4. Woodson, S. A. (2005) Current Opinion in Chemical Biology 9, 104109. 5. Thirumalai, D. & Hyeon, C. (2005) Biochemistry 44, 4957-4970. 6. Gruebele, M. (2002) Current Opinion in Structural Biology 12, 161168. 7. Plotkin, S. S. & Onuchic, J. N. (2002) Quarterly Reviews of Biophysics 35, 111-167. 8. Smith, G., Lee, K.-T., Qu, X., Pesic, J., Xie, Z., Sosnick, T. R., Pan, T., & Scherer, N. F. (2007) submitted to J. Mol. Biol. 9. Russell, R., Zhuang, X. W., Babcock, H. P., Millett, I. S., Doniach, S., Chu, S. & Herschlag, D. (2002) Proceedings of the National Academy of Sciences of the United States of America 99, 155-160. 10. Thirumalai, D., Lee, N., Woodson, S. A., Klimov, D. K. (2001) Annu. Rev. Phys. Chem 52, 751-762. 11. Eigen, M. & Hammes, G. G. (1960) Journal of the American Chemical Society 82, 5951-5952. 12. Munoz, V., Thompson, P. A., Hofrichter, J. & Eaton, W. A. (1997) Nature 390, 196-199. 13. Krantz, B. A. & Sosnick, T. R. (2000) Biochemistry 39, 11696-11701. 14. Fang, X. W., Pan, T. & Sosnick, T. R. (1999) Nature Structural Biology 6, 1091-1095. 15. Russell, R., Millettt, I. S., Tate, M. W., Kwok, L. W., Nakatani, B., Gruner, S. M., Mochrie, S. G. J., Pande, V., Doniach, S., Herschlag, D. & Pollack, L. (2002) Proceedings of the National Academy of Sciences of the United States of America 99, 4266-4271. 16. Downey, C. D., Fiore, J. L., Stoddard, C. D., Hodak, J. H., Nesbitt, D. J. & Pardi, A. (2006) Biochemistry 45, 3664-3673. 17. Chandler, D. (1987) Introduction to modern statistical mechanics (Oxford University Press, New York). 18. McKinney, S. A., Freeman, A. D. J., Lilley, D. M. J. & Ha, T. J. (2005) Proceedings of the National Academy of Sciences of the United States of America 102, 5715-5720. 19. Cosa, G., Zeng, Y. N., Liu, H. W., Landes, C. F., Makarov, D. E., Musier-Forsyth, K. & Barbara, P. F. (2006) Journal of Physical Chemistry B 110, 2419-2426. 20. Zhuang, X. W. (2005) Annual Review of Biophysics and Biomolecular Structure 34, 399-414. 21. Rueda, D., Bokinsky, G., Rhodes, M. M., Rust, M. J., Zhuang, X. W. & Walter, N. G. (2004) Proceedings of the National Academy of Sciences of the United States of America 101, 10066-10071. 22. Ha, T., Zhuang, X. W., Kim, H. D., Orr, J. W., Williamson, J. R. & Chu, S. (1999) Proceedings of the National Academy of Sciences of the United States of America 96, 9077-9082. 23. Zhuang, X. W., Bartley, L. E., Babcock, H. P., Russell, R., Ha, T. J., Herschlag, D. & Chu, S. (2000) Science 288, 2048-2051. 24. Smith, G. J., Sosnick, T. R., Scherer, N. F. & Pan, T. (2005) Rna-a Publication of the Rna Society 11, 234-239. 25. Hill, T. L. & Hill, T. L. (1989) Free energy transduction and biochemical cycle kinetics (Springer-Verlag, New York). 26. Fang, X. W., Thiyagarajan, P., Sosnick, T. R. & Pan, T. (2002) Proceedings of the National Academy of Sciences of the United States of America 99, 8518-8523. 27. Fang, X. W., Golden, B. L., Littrell, K., Shelton, V., Thiyagarajan, P., Pan, T. & Sosnick, T. R. (2001) Proceedings of the National Academy of Sciences of the United States of America 98, 43554360. 28. Kwok, L. W., Shcherbakova, I., Lamb, J. S., Park, H. Y., Andresen, K., Smith, H., Brenowitz, M. & Pollack, L. (2006) Journal of Molecular Biology 355, 282-293. 29. Lambert, M. N., Vocker, E., Blumberg, S., Redemann, S., Gajraj, A., Meiners, J. C. & Walter, N. G. (2006) Biophysical Journal 90, 3672-3685. 30. Kazantsev, A. V., Krivenko, A. A., Harrington, D. J., Holbrook, S. R., Adams, P. D. & Pace, N. R. (2005) Proceedings of the National Academy of Sciences of the United States of America 102, 13392-13397. 31. Fang, X. W., Srividya, N., Golden, B. L., Sosnick, T. R. & Pan, T. (2003) Journal of Molecular Biology 330, 177-183. 32. Tietz, C., Schuler, S., Speck, T., Seifert, U. & Wrachtrup, J. (2006) Physical Review Letters 97, 050602. 33. Min, W. & Xie, X. S. (2006) Physical Review E 73, 010902(R). Tables Table 1 EFRET values at the peak positions of the EFRET histograms in Figs. 2-B and 3-B [Mg2+] 0.01mM 0.1mM 0.4mM 1mM EFRET Values 0.19 0.21 0.25 0.25 state I 0.41 0.45 state II 0.62 0.7 state III 0.7 0.76 0.8 0.85 state IV Error: +/- 0.02(upper bound). The EFRET states are separated into four groups (I-IV) according to their structural relation by electrostatic relaxation. Figure Captions Figure 1 Schematic of the periodic [Mg2+]-jump experiment and cycling of the energy landscape. A): [Mg2+] profile applied in the experiments. The lengths of the high and low [Mg2+] intervals are both 10 sec with 50uL/min flow rate for all the experiments reported here. The solid line shows the idealized [Mg2+] change over time. The overlaid dotted data shows the averaged brightness of isolated Cy3 molecules in one field of view. B): Schematic free energy landscape for the periodic [Mg2+]-jump experiment. Circles represent the population in each EFRET level. The vertical dashed lines show that the EFRET value of each EFRET state shifts to a higher value at higher [Mg2+] due to electrostatic relaxation. The solid arrows (lower left panel) represent the folding pathways observed for molecules starting from the low or high EFRET state. These two cases are separated by a high barrier associated with the hidden DOF. The dashed double arrows are meant to indicate that transitions over the high barrier of the hidden DOF are seldom observed within the 10-sec [Mg2+] step. The number of basins, exact barrier heights or well depths, EFRET values and population at each EFRET state are different for the three [Mg2+]-jump conditions. (Note: the coordinates to the left and right of the large barrier are different due to the presence of the state of the hidden DOF. The figure is a 1-dim representation of a 2-dim energy landscape.). C) Locations of the L18 loop (Cy3, green spheres) and 3’ end (Cy5, red spheres) on the tertiary structure model of Cthermo from ADDIN EN.CITE <EndNote><Cite><Author>Kazantsev</Author><Year>2005</Year><RecNum>35</Rec Num><record><rec-number>35</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kazantsev, A. V.</author><author>Krivenko, A. A.</author><author>Harrington, D. J.</author><author>Holbrook, S. R.</author><author>Adams, P. D.</author><author>Pace, N. R.</author></authors></contributors><authaddress>Pace, NR
Univ Colorado, Dept Mol Cellular & Dev Biol, Boulder, CO 80309 USA
Univ Colorado, Dept Mol Cellular & Dev Biol, Boulder, CO 80309 USA
Stanford Univ, Stanford Synchrotron Radiat Lab, Menlo Pk, CA 94025 USA
Univ Calif Berkeley, Lawrence Berkeley Lab, Phys Biosci Div, Berkeley, CA 94720 USA
Univ Calif Berkeley, Lawrence Berkeley Lab, Computat Crystallog Initiat, Berkeley, CA 94720 USA</auth-address><titles><title>Crystal structure of a bacterial ribonuclease P RNA</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondarytitle></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title><abbr1>Proc. Natl. Acad. Sci. U. S. A.</abbr-1><abbr-2>Proc Natl Acad Sci U S A</abbr-2></periodical><pages>1339213397</pages><volume>102</volume><number>38</number><keywords><keyword>ri bozyme</keyword><keyword>rna crystallography</keyword><keyword>trna processing</keyword><keyword>metal-ion binding</keyword><keyword>large ribosomal-subunit</keyword><keyword>pre-transferrna</keyword><keyword>bacillus-subtilis</keyword><keyword>activesite</keyword><keyword>tertiary interaction</keyword><keyword>angstrom resolution</keyword><keyword>escherichiacoli</keyword><keyword>magnesium-ions</keyword><keyword>precursor trna(asp)</keyword></keywords><dates><year>2005</year><pubdates><date>Sep 20</date></pub-dates></dates><isbn>00278424</isbn><accession-num>ISI:000232115100009</accession- num><urls><related-urls><url><Go to ISI>://000232115100009</url></relatedurls></urls><language>English</language></record></Cite></EndNote> (30) . Figure 2 T h e 0 . 0 1 ”!0 . 1 m M [ M g 2 + ] - j u m p e x p e r i m e n t . ( A ) : T y p i c a l s i n g l e - m o l e c u l e t r a j e c t o r y . T h e [ M g 2 + ] p r o f i l e ( s o l i d s q u a r e w a v e ) s u p e r i m p o s e d o n t h e F R E T t r a j e c t o r y f o r a s i n g l e R N A m o l e c u l e . ( B ) : C u m u l a t i v e E F R E T h i s t o g r a m s f o r f o l d i n g a n d u n f o l d i n g . T h e h i s t o g r a m s are constructed from all the single-molecule EFRET trajectories in one field of view (~100 RNA molecules are observed simultaneously). Insets: Equilibrium EFRET histograms (C): Population relaxation kinetics of the low (black) and high (gray) EFRET states. These curves are constructed by sorting all folding and unfolding trajectory segments according to EFRET state prior to the [Mg2+]-jump, and calculating the fraction of molecules that occupy this state at each later time point. 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Pž cž wž yž ¨ž »ž ¼ž ½ž ž Æž óž ôž üž Ÿ Ÿ • • • • • • • KŸ LŸ WŸ XŸ YŸ kŸ lŸ h? hŒm6 6 •CJ aJ h? hŒm6 CJ aJ j h? hÎUq CJ U aJ h? hÎUq CJ aJ h? hZ ª 5 •>* CJ aJ h? h» Ó 5 •>* CJ aJ h? hŸY ‚Ÿ ŸŸ ØŸ õêßÔɾ꾳Ծ¨³¾’¨„vk\k\QEQ CJ aJ h? h)Y• CJ aJ h? hOKO CJ aJ h? hlB CJ aJ h? h.a¿ CJ aJ h? h L© CJ aJ h? ha/˜ CJ aJ h? h·6ª CJ aJ h? heD© CJ aJ h? hûkc CJ aJ ØŸ ýŸ þŸ > t u x › ¾ ¿ Á ð ü ¡ #¡ H¡ I¡ L¡ €¡ Ÿ¡ ¡ £¡ ¢ š¢ é¢ ê¢ í¢ û¢ 9£ N£ O£ Q£ Z£ •£ ©£ ª£ -£ þ£ ¤ ¤ ¤ =¤ I¤ J¤ M¤ Œ¤ ¥¤ ¦¤ ¨¤ [¥ ª¥ «¥ ®¥ ¦ (¦ )¦ ,¦ P¦ |¦ î¦ =§ >§ B§ ¿§ Þ§ ߧ 㧠¨ >¨ ?¨ B¨ óèÜèóèÜèóèÜèóèÜèó èÜèóèÜèóèóèÜèÑÅѹÑèóèÜèóèÜèóèÜèóèÜèóèÜèóèÜèóèóèÜèóèÜèóèÜ h? • hxar 5 •CJ aJ h? • hxar 6 •CJ aJ h? • hxar CJ aJ h? • hŒm6 5 •CJ aJ h? • hŒm6 CJ aJ h? • hŒm6 6 •CJ aJ I¹£ ¤ [¤ ´¤ º¥ 8¦ ¢¦ N§ ï§ L¨ • • • • • • • • • ý ¢ © Á© Cª ò ·ª 1« Ó« ò Ÿ¬ Ô- £® ò ò ò ò å Š¯ ˯ ò ò ò ò ¯ ò ò ò dŒm6 C- å ί ò ò ò ̯ Ö¯ ò .° ò ò ò ò ò dà ò í gd"~2 g „Ð „0ý^„Ð `„0ýgdŒm6 B¨ ª¨ ù¨ ú¨ þ¨ b© ±© ²© µ© 7ª …ª ©ª ªª -ª ܪ « t« ë Ä« Ç« @¬ •¬ •¬ “¬ 9- ±- Ä- Å- È- A® •® ‘® •® ñ® ¯ +ª 2ª 3ª - 4- 5- ¯ ¯ f¯ }¯ ~¯ •¯ ª¯ »¯ ¼¯ ¿¯ ̯ ͯ ί Ö¯ õÝõéõÝõéõÝõéõéõÝõéõÝõéõÝõéõÝõéõÝõéõÝõéõÝõéõÝõÎõ©ž’ • h"~2 CJ H* aJ h? • h"~2 CJ aJ h? • h"~2 5 •CJ aJ h? • h"~2 5 •>* CJ aJ h? • hnNR CJ aJ j h? • hÎUq CJ U aJ h? • hŒm6 5 •CJ aJ h? • hŒm6 6 •CJ aJ h? • hŒm6 CJ aJ 9㯠° ° ° 1° 3° O° T° ç° ë° \± ]± d± l± m± u± v± б ѱ Ó± Õ± -² ² õéÞõÒõéõéõĶ¨‘Štht]tRFRF • hU I CJ H* aJ h? • hU I CJ aJ h? • hŒM› CJ aJ h? • hª â CJ H* aJ h? • hª â CJ aJ h? • h· ³ CJ aJ ݯ ߯ h? 㯠õéõÝõé ˆ± “± h? •± ʱ ͱ • • • • • • • • • • h? hU I hU I h•?ò h•O hU I h"~2 h"~2 hã0f h"~2 h"~2 h? 5 •CJ aJ h? CJ aJ h? 5 •>* CJ aJ h? 5 •>* CJ aJ h? 5 •>* CJ aJ h? CJ H* aJ h? CJ aJ h? CJ H* aJ h? CJ aJ .° 5° <° ó ó B° H° L° ó M° ó ó ó $ $ If a$ gdÄ M° N° [° 7 $ # „q „q s Ö $ If ]„q ^„q a$ gdÄ - È Öˆ kdR 8 p ¨ $ $ If – à d œ € 8 8 „ t à Ö0 ÿ ÿ ÿ ÿ ÿ ÿ Ö ÿ s aö s ytÄ [° `° e° ó ÿ ÿ ÿ j° ÿ ÿÿÿÿÿ Ö ÿ ÿ ÿ ÿÿÿÿÿ4Ö o° w° ó 8 ÿÿÿÿ ÿ ÿ ÿ ó ÿ ÿ 4Ö 8 ÿÿÿÿ ÿ ÿ ÿ Ö ó 8 ö ÿ ö ÿ ö ÿ ó Ö ÿ $ $ If a$ gdÄ w° x° y° z° {° 5 ) ) ) $ $ If $ $ If a$ gdÄ - É –s 4 Ö kd Öˆ 8 p ¨ à d œ ì 8 8 8 „ t à Ö0 ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ Ö ÿ ÿ ÿ s aö s ytÄ {° €° …° Ž° •° É kd s 4 Ö ÿ ÿ Ö ÿ ÿ ó $ ÿ ÿ4Ö 8 ÿ ÿ ÿ ÿ ÿ 4Ö ó – $ If Öˆ ÿ ÿ Ö ÿ ó 8 p ¨ 8 ö ÿ ö ÿ ) ö ÿ Ö ÿ à d œ 8 8 „ t à Ö0 ÿ ÿ ÿ ÿ ÿ ÿ Ö ÿ s aö s ytÄ - ÿ ÿ ÿ 8 8 ÿ ÿ ÿ ÿ Ö ÿ ÿ ÿ ÿ ÿ ÿ4Ö ÿ 8 ÿ ÿ 4Ö ÿ ÿ ÿ Ö ö ÿ ö ÿ ö ÿ Ö ÿ ° $ $ If ›° ¥° ó ó a$ gdÄ - •° ó •° ‘° ’° ó — ó ó $ $ If a$ gdÄ ¥° ¦° §° «° °° 5 ) ) ) s $ 4 $ If Ö a$ gdÄ - É kdn $ Öˆ $ If 8 p ¨ – à d œ 8 8 8 „ t Ö0 ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ ÿ Ö ÿ ÿ ÿ s aö s ytÄ °° ´° ¹° ° ð É kd s 4 Ö 8 ÿ à ÿ Ö ÿ ÿ ó $ ÿ ÿ ÿ ÿ4Ö ÿ 8 ÿ ÿ 4Ö ó – $ If Öˆ ÿ ÿ Ö ÿ ó 8 p ¨ ö ÿ ö ÿ ) ö ÿ Ö ÿ à d œ 8 8 „ t à Ö0 ÿ ÿ ÿ ÿ ÿ ÿ Ö ÿ s aö s ytÄ - ÿ ÿ ÿ 8 8 ÿ ÿ ÿ ÿ Ö ÿ ÿ ÿ ÿ ÿ ÿ4Ö ÿ 8 ÿ ÿ 4Ö ÿ ÿ ÿ Ö ö ÿ ö ÿ ö ÿ Ö ÿ $ $ If a$ gdÄ Ã° Ä° m± Ò¿ Ó¿ Nu Ou } } ì• í• Ø• Ü• Þ• â• ä• è• ê• î• ð• • • -• • ÷ ï ç ß ß × × Ò ÷ ÷ ÷ Ð Ð Ð Ð Ð Ð Ð Ð È Ð Ð Ð $ a$ gd!+Á gd¸/û dà gd€Z— dà gdU I dà gd×$² dà gdnNR dà gd"~2 ² "² +² 5² 8² 9² ¡² £² -³ ³ ³ "³ (³ A³ V³ X³ Y³ l³ •³ ™³ ¡³ º³ ʳ γ Þ³ â³ ´ ´ -´ ±´ Ï´ ø´ µ =µ Gµ Hµ Oµ bµ õíõíâõÖõËÀ˵ªµžµ“µ‡|qµ‡µ‡µžµ‡µfµfµf µf h? • hóEF CJ aJ h? • h SÜ CJ aJ h? • hVnÑ CJ aJ h? • h×$² CJ H* aJ h? • h8BÚ CJ aJ h? • h×$² CJ H* aJ h? • h 7Ó CJ aJ h? • h×$² CJ aJ h? • hi~Å CJ aJ h? • h;*Ñ CJ aJ h? • hU I CJ H* aJ h? • h$_ú CJ aJ hÄAš CJ aJ h? hU I CJ aJ %bµ fµ tµ •µ ”µ šµ œµ ϵ Þµ áµ åµ ¶ ¶ /¶ 1¶ 7¶ J¶ Ÿ¶ ¯¶ ƶ · · ;· <· Y· Z· Œ· •· Ê¿ Ë¿ Ï¿ п Ñ¿ Ò¿ Ó¿ õêßÔßÈ߽߱߱ßȦ›ß• ß…ßzozoz`z`z`zßY • h? h×$² j h? h—3= CJ U aJ h? h8BÚ CJ aJ h? h—3= CJ aJ h? hKu² CJ aJ h? hÁIª CJ aJ h? hyWÖ CJ aJ h? h UG CJ aJ h? h×$² CJ H* aJ h? h 7& CJ aJ h? h×$² CJ H* aJ h? h$_ú CJ aJ h? h×$² CJ aJ h? hóEF CJ aJ h? h^ Û CJ aJ "Ó¿ Û¿ À $À (À ®À ²À ŽÁ – àÁ / 3 •Â œÂ •Â ¡Â Ñ ó õ ù ÿ à "à Xà fà jà •Ã ƒÃ ‰Ã äÃ Ä t 1t 3t ?t Ft Gt Pt Ut Yt pt tt zt {t ~t „t Št Žt ¥t ©t ²t ùt óèÝÑÝÑÝźÝÅݺÝÅݯÝÅݯݤÝÅÝÑݤݢÝÑ— ݺŒÝŒÝÅÝŒºŒÝŒÝÅºÝ h? • hrqš CJ aJ h? • hþlƒ CJ aJ U h? • h 2l CJ aJ h? • hyXÐ CJ aJ h? • hÊMn CJ aJ h? • h • CJ H* aJ h? • h • CJ H* aJ h? • h • CJ aJ h? • hŒM› CJ aJ h? • hà(ï 5 •CJ aJ 3imated by exponential fits after the 1-2 sec. [Mg2+]-transition time. Unfolding from the high (C1) or low (C2) EFRET states; Folding from the high (C3) or low (C4) EFRET state. Circles after the split of the time axis show the equilibrium population distributions. Vertical lines at ~2sec show when the [Mg2+]-transition period ends. • • • • • • • • • • • • • • • Á Figure 3 [Mg2+]-jump experiments for 0 . 0 1 ”!0 . 4 m M ( A 1 , B 1 , B 2 , C 1 ) a n d 0 . 0 1 ”!1 . 0 m M ( A 2 , B 3 , B 4 , C 2 ) . A ) : R e p r e s e n t a t i v e s i n g l e - m o l e c u l e t r a j e c t o r i e s . T h e i n s e t s o f ( A 1 ) s h o w t h e s m o o t h E F R E T c h a n g e ( d o t s ) d u e t o e l e c t r o s t a t i c r e l a x a t i o n o v e r l a p w i t h t h e m e a s u r e d [ M g 2 + ] p r o f i l e s ( s o l i d l i n e s ) . T h e last high [Mg2+] step of the lower trajectory in (A2) shows a rarely observed transition (arrow) over the high barrier associated with the hidden DOF (Fig. 1-B) whose signature is a transition from the state IV to state III. B): Cumulative EFRET histograms for molecules folding from the high(B1,B3) or low(B2,B4) EFRET states. Insets: Equilibrium EFRET histograms. In (B, C), blue-state I; green-state II; red-state III; purple-state IV (state definition: ref. Table 1). C): Population relaxation kinetics for molecules folding from the low EFRET state. Molecules starting from the high EFRET state only show occasional transitions to state III and negligible transitions to other EFRET states (data not shown). Two-state behavior similar to that observed in the 0. e o f n x b o o p e r i m s e r v e r t h e t s h o 0 e n t ( F i g s . 2 d a t t h e l o w s e t w o j u m p c w n ) . 1 B [ o ”!0 . 1 m M 1 , C 1 , C 2 ) i s M g 2 + ] i n t e r v a l n d i t i o n s ( d a t a F i g u r e 4 C o n n e c t i v i t y b e t w e e n E F R E T s t a t e s f o r t h e t h r e e [ M g 2 + ] - j u m p c o n d i t i o n s : A ) [ M g 2 + ] = 0 . 0 1 ”!0 . 1 m M ; B ) [ M g 2 + ] = 0 . 0 1 ”!0 . 4 m M / 1 . 0mM. The solid double-headed arrows represent RNA conformational fluctuations that happen during the constant [Mg2+] interval and involve barrier crossing with time constants on the order of seconds. The solid single-headed arrows represent electrostatic relaxation of the RNA structure, which follows the [Mg2+]transition curve. In (B), for the [Mg2+ b s [ s e d c d a t M i l i r o r r i a t e g 2 + m u l e c t f f e o s s u b l u u u v &v (v b„W„Wb„y • h+ e CJ • h> e r I ] t a r o r e i n e 2u 0v aJ ] = c r o I a l t r a n n e o u s t a t n t f g p r h e a d 4u 5u ^v `v h? 0 . 0 1 ”!1 s s i n g s o h a p s i t i o n s l y w i i c r e l r o m o t o c e s s e e ùt u 6u Mu Nu bv dv fv h? . 0 m M b e t w p e n s t i m t h t a x a t h e r s ( s c e e d e , h e i o b a h o o n d i t i o n , n s t a t e I u r i n g t h e Ou nv Xu vv [u žv Wu pv t h e a n d n . T h i s i s r r i e r w n a s s o l i d ]u v -v õêßÔßȽ²ß§›„ymy„b„bW„ à CJ aJ h? • hû!š CJ H* aJ h? • hû!š CJ aJ h? • h€Z— CJ aJ h? • h€Z— 5 •CJ aJ h? • hyXÐ 5 •CJ aJ h? • h^xÊ CJ aJ h? • h¦}' CJ aJ h? • hþlƒ CJ aJ h? • h • CJ H* aJ h? • hÆLÉ CJ aJ h? • h • CJ aJ h? • hÊMn CJ aJ h? • h«5‰ CJ aJ -žv Øv Üv w w $w ,w Äw Èw Øw øw x x $x [x cx qx ˜x Ÿx x Çx Ìx áx ãx óx ÷x y y y y y !y &y .y 0y õêßÔßÈß¼ßÔß¼±ß¦ß›ß›ß…ß êyên¦nc¦cX¦ h? • hÞ^è CJ aJ h? • h/`‹ CJ aJ h? • hS ø CJ aJ h? • h€Z— CJ H* aJ h? • h^b± CJ aJ h? • hCJ aJ h? • hû!š CJ aJ h? • hÆH· CJ aJ h? • hqHC CJ aJ h? • h•- CJ H* aJ h? • h•- CJ H* aJ h? • hÊMn CJ aJ h? • h•- CJ aJ h? • h€Z— CJ aJ h? • h•V CJ aJ "0y :y =y Ay Hy Jy Ry ^y _y cy py Úy ôy z z !z %z z .z Oz Sz Zz _z -z ±z ¸z õêÞÓêȽȱȦț…y…ncWcLcWc h? • h•Nc CJ aJ h? • hô$å CJ H* aJ h? • hô$å CJ aJ h? • h^b± CJ aJ h? • h - CJ H* aJ h? • h - CJ aJ h? • hÔ Á CJ aJ h? • hd(… CJ aJ h? • hbtÒ CJ aJ h? • h€Z— CJ H* aJ h? • hÆH· CJ aJ h? • h€Z— CJ aJ h? • h/`‹ CJ aJ h? • hS ø CJ H* aJ h? • hS ø CJ aJ h? • hÞ^è CJ aJ ¸z Éz Ëz Íz ùz <| B| D| J| N| †| Š| ž| ¼| Ú| } } } } } B} J} b} j} |} €} ž} õêßÔɾɾÉ߲ߧÉßœ•‰}rf r[rOr h? • h×$² CJ H* aJ h? • hN4ð CJ aJ h? • h×$² CJ H* aJ h? • h×$² CJ aJ h? • h= – 5 •CJ aJ h? • h×$² 5 •CJ aJ h? • hU I h? • h€Z— CJ aJ h? • hŸ]p CJ aJ h? • h - CJ H* aJ h? • h^CË CJ aJ h? • h@f[ CJ aJ h? • h f³ CJ aJ h? • h - CJ aJ h? • hô$å CJ aJ h? • hû"W CJ aJ ž} ¨} ²} ¶} Ô} Þ} â} ~ ~ S~ m~ q~ s~ }~ ‚~ ˆ~ ~ Ù~ à~ • • 5• 7• K• S• W• [• ^• € € ,€ ”€ ž€ Ê€ ΀ Ò€ h• ‚ Œ Œ ,Œ õêÞõêÞêÓêȽ±¦½ê›êÓêêÞê…½z½±½z½¦½±o½zmz½ U h? • hÍ$Þ CJ aJ h? • hÀ ` CJ aJ h? • h h CJ aJ h? • hÓeu CJ aJ h? • hâEb CJ aJ h? • h!"· CJ aJ h? • h¦"ƒ CJ H* aJ h? • h¦"ƒ CJ aJ h? • hh ø CJ aJ h? • hN4ð CJ aJ h? • h×$² CJ H* aJ h? • h×$² CJ aJ h? • hšR¦ CJ aJ (d arrows) and thus is represented by hollow singleheaded arrows. States III and III* in (B) have indistinguishable EFRET values within experimental error but differ in dynamic behavior due to difference in hidden DOF. The transitions between III and III* are very rarely observed, thus not represented by arrows. For EFRET states that are not connected by single-headed arrows at [Mg2+]-jump, direct transitions between them during [Mg2+]-transition time are rarely observed in experiments. Figure p e r f r a E F R u n f i n e i t p e r 5 i c E o a h i P a g e Relaxation k o d l e n g t i o n a l T s t a t e l d i n g f 0 . 0 1 ”!0 e r 1 0 ( o d s . P AGE i n e t t h . p o p u f o r r o m . 1 m M Ë%) o 14 of i c s S h o w l a t i m o l t h e j u m r 2 0 NUMPAGES a n o e l p r e a n c u o w e ( X 20 d e r e o f l e s E F x p e ) s p e n t h e t h e t h R E T r i m e c o d e n t o n l o w a t a r e s t a t e e n t w i t h n d , :Œ @Œ JŒ sŒ uŒ yŒ Œ šŒ ÛŒ :• ?• C• l• s• €• ‚• ˆ• ‘• °• ´• ¶• • Ç• ê• ë• ì• í• õ• RŽ õêßêßÓßÈß½²¦²ê²š„y²šny„²êc WL h? • hÞ6s CJ aJ h? • hÞ6s 5 •CJ aJ h? • hÛK. 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Q c u ‡ v ˆ — ¦ ¸ Ê Ü î = O a § ¹ Ë Ý ï ¨ º Ì Þ ð © » Í ß ñ à ò ! . @ " / A # 0 B $ 1 C % 2 D & 3 ' 4 ( 5 ) 6 * 7 + 8 J , 9 K E F G H I R S T U V W X Y Z þÿÿÿ\ ] ^ ýÿÿÿýÿÿÿýÿÿÿg j þÿÿÿê ù l m n o p ÿÿÿw x y z { | } ~ • € R o o t E n t r y À ÿÿÿÿÿÿÿÿÿÿÿÿ o c u m e n t ÿÿÿÿÿÿÿÿ c t P o o l F pm:ž È i @ : L ; M _ q < N ` r = > O a s P b t ? Q þÿÿÿ v ý ÿÿÿÿÿÿÿÿ D a t a [ W o r d D ;´ O b j e ÿÿÿÿ 4 3 7 3 À F ÐÖ ž ÐÖ ž È ÐÖ ž È pm:ž È È _ 1 2 5 0 9 4 ÿÿÿÿÿÿÿÿ Î O l e ÿÿÿÿÿÿÿÿÿÿÿÿ O b j C o m p ÿÿÿÿ i þÿÿÿ ÿÿÿÿ þÿÿÿþÿÿÿ O b j I n f o ÿÿÿÿ þÿÿÿ þÿÿÿ þÿÿÿ þÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ þÿ ÿÿÿÿ Î À F MathType 5.0 Equation EF MathType Equation.DSMT4 ô9²q ÃÊ Ìæ D © ¤æ DSMT5 WinAllBasicCodePages Times New Roman Symbol Courier New MT Extra !/E•D/APô G_APò-APô A ôEô%ô•B_A ô C_A ô•Eô*_Hô•A ô @ô•A•Hô A*_D_Eô_Eô_A ‹k"? 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