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<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Archiving and Interchange DTD v2.3 20070202//EN" "archivearticle.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" article-type="research-article"><?properties open_access?><front><journal-meta><journal-id journal-id-type="nlm-ta">Nucleic Acids Res</journal-id><journal-id journal-id-type="publisher-id">Nucleic Acids Research</journal-id><journal-title>Nucleic Acids Research</journal-title><issn pub-type="ppub">0305-1048</issn><issn pub-type="epub">1362-4962</issn><publisher><publisher-name>Oxford University Press</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">16822858</article-id><article-id pub-id-type="pmc">PMC1488884</article-id><article-id pub-id-type="doi">10.1093/nar/gkl422</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Secondary structure effects on DNA hybridization kinetics: a solution versus surface comparison</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Gao</surname><given-names>Yang</given-names></name></contrib><contrib contrib-type="author"><name><surname>Wolf</surname><given-names>Lauren K.</given-names></name></contrib><contrib contrib-type="author"><name><surname>Georgiadis</surname><given-names>Rosina M.</given-names></name><xref ref-type="corresp" rid="cor1">*</xref></contrib><aff><institution>Department of Chemistry, Metcalf Center for Science and Engineering, Boston University</institution><addr-line>590 Commonwealth Avenue, Boston, MA 02215, USA</addr-line></aff></contrib-group><author-notes><corresp id="cor1"><sup>*</sup>To whom correspondence should be addressed. Tel: +1 617 353 2500; Fax: +1 617 353 6466; Email: <email>rgeorgia@bu.edu</email></corresp></author-notes><!--For NAR: both ppub and collection dates generated for PMC processing 1/27/05 beck--><pub-date pub-type="collection"><year>2006</year></pub-date><pub-date pub-type="ppub"><year>2006</year></pub-date><pub-date pub-type="epub"><day>5</day><month>7</month><year>2006</year></pub-date><volume>34</volume><issue>11</issue><fpage>3370</fpage><lpage>3377</lpage><history><date date-type="received"><day>21</day><month>2</month><year>2006</year></date><date date-type="rev-recd"><day>05</day><month>5</month><year>2006</year></date><date date-type="accepted"><day>27</day><month>5</month><year>2006</year></date></history><copyright-statement>© 2006 The Author(s)</copyright-statement><copyright-year>2006</copyright-year><license license-type="openaccess"><p>This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by-nc/2.0/uk/"/>) which permits unrestricted non-commerical use, distribution, and reproduction in any medium, provided the original work is properly cited.</p></license><abstract><p>The hybridization kinetics for a series of designed 25mer probe–target pairs having varying degrees of secondary structure have been measured by UV absorbance and surface plasmon resonance (SPR) spectroscopy in solution and on the surface, respectively. Kinetic rate constants derived from the resultant data decrease with increasing probe and target secondary structure similarly in both solution and surface environments. Specifically, addition of three intramolecular base pairs in the probe and target structure slow hybridization by a factor of two. For individual strands containing four or more intramolecular base pairs, hybridization cannot be described by a traditional two-state model in solution-phase nor on the surface. Surface hybridization rates are also 20- to 40-fold slower than solution-phase rates for identical sequences and conditions. These quantitative findings may have implications for the design of better biosensors, particularly those using probes with deliberate secondary structure.</p></abstract></article-meta></front><body><sec><title>INTRODUCTION</title><p>The process of hybridization, in which an oligonucleotide probe recognizes and binds to its complementary target, is the most vital component of DNA- and RNA-based biosensor technology. This technology, often used in conjunction with microarray surfaces, is being increasingly applied in gene sequencing, gene expression profiling and drug discovery. Factors such as ionic strength, sequence composition and temperature, which affect both surface (<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>) and solution-phase hybridization (<xref ref-type="bibr" rid="b3">3</xref>,<xref ref-type="bibr" rid="b4">4</xref>), have been characterized extensively. In fact, solution-phase hybridization studies have been so extensive that algorithms have been derived to quantitatively predict the thermodynamics of duplex formation for selected input sequences and conditions (<xref ref-type="bibr" rid="b5">5</xref>,<xref ref-type="bibr" rid="b6">6</xref>).</p><p>Similarly, algorithms have been designed to predict the folding or secondary structure present in single-stranded oligomers under various solution conditions (<xref ref-type="bibr" rid="b5">5</xref>,<xref ref-type="bibr" rid="b7">7</xref>,<xref ref-type="bibr" rid="b8">8</xref>). Not only does oligonucleotide secondary structure play an important role in biological recognition processes, but is also known to be an additional factor in duplex hybridization (<xref ref-type="bibr" rid="b9">9</xref>–<xref ref-type="bibr" rid="b11">11</xref>). Few studies, however, have attempted to quantitatively characterize the effects of sequence secondary structure on the kinetics and thermodynamics of hybridization in solution (<xref ref-type="bibr" rid="b12">12</xref>–<xref ref-type="bibr" rid="b15">15</xref>), or on the surface (<xref ref-type="bibr" rid="b16">16</xref>). With the advent of structured-probe biosensors, such as those incorporating hairpins, molecular beacons or aptamers, it becomes more important to understand these structural effects.</p><p>Generally, the intramolecular base pairs involved in secondary structure, stabilize single-strand conformation, creating a higher energy barrier to intermolecular hybridization. This, in turn, can slow hybridization kinetics. In practical biosensor applications, these effects are lessened by designing shorter single-stranded probe and target molecules or by increasing the ‘incubation’ temperature. Nevertheless, reducing strand length can also reduce biosensor detection sensitivity and increasing temperature, even to physiological values, does not always eliminate all effects (<xref ref-type="bibr" rid="b17">17</xref>). In addition, biosensors employing structured probes cannot be operated at high temperatures and maintain performance. As a result, there is a need for quantitative characterization of secondary structure effects on hybridization, particularly surface hybridization, using biosensor-relevant conditions.</p><p>To this end, we have systematically studied the effect of secondary structure on DNA–DNA hybridization kinetics both in solution and on the surface under identical conditions. We have used <italic>in situ</italic> UV absorbance and surface plasmon resonance (SPR) spectroscopy, respectively, to investigate duplex formation in a series of probe–target pairs containing varying well-defined degrees of secondary structure. Hybridization kinetic rates were suppressed as a function of individual strand secondary structure in a similar, clearly defined manner in solution and on the surface. Target hybridization on the surface was also 20–40 times slower than in solution for our system. In addition, probe and target pairs containing large amounts of secondary structure were shown to hybridize by a more complex mechanism than traditional two-state duplex formation. We have proposed, instead, a mechanism of fast nucleation and slow partial strand displacement.</p></sec><sec sec-type="materials|methods"><title>MATERIALS AND METHODS</title><sec sec-type="materials"><title>Materials</title><p>All oligonucleotides were purchased from Integrated DNA Technologies (IDT). The sequences are listed in <xref ref-type="table" rid="tbl1">Table 1</xref>. All probe sequences employed in surface studies were modified at the 5′ terminus with a six-carbon linker and thiol group (HS-(CH<sub>2</sub>)<sub>6</sub>–). These sequences were received with a protecting group attached via disulfide bond. Before use, the protective disulfide bond was cleaved by incubating the oligonucleotides with 0.04 M DTT (Amersham Biosciences) in 0.17 M sodium phosphate buffer (pH = 8.0; Sigma) at room temperature for at least 16 h. The cleaved molecules were separated on a size-exclusion NAP-10 column (Amersham Biosciences). The concentration of thiolated DNA recovered from the column was determined by UV absorbance measurements at 260 nm (Varian Cary 100). All target and non-thiolated probe sequences employed in solution-phase studies were used as received.</p><p>Other chemicals employed in both solution-phase and surface studies were purchased from Sigma and used as received. These include mercaptohexanol (MCH), potassium dihydrogen phosphate (KH<sub>2</sub>PO<sub>4</sub>), sodium chloride (NaCl), ethylenediaminetetraacetic acid (EDTA), Trizma hydrochloride, Trizma Base and SDS. All buffers and immobilization solutions were prepared with 18 MΩ·cm distilled water.</p></sec><sec><title>Sequence selection</title><p>In order to systematically study the effects of secondary structure on DNA hybridization kinetics, we designed a series of short oligomers using mFold (<xref ref-type="bibr" rid="b5">5</xref>,<xref ref-type="bibr" rid="b7">7</xref>,<xref ref-type="bibr" rid="b8">8</xref>). The selected 25mer sequences, shown in <xref ref-type="table" rid="tbl1">Table 1</xref>, contain varying numbers of base pairs involved in intramolecular folding. The nucleobases participating in the secondary structure predicted by mFold are underlined for clarity. Although some of these sequences were predicted to have more than one possible conformation, only the lowest energy structures are considered (and underlined) here. Under the conditions employed in these studies, P<sub>0</sub> and T<sub>0</sub> have no secondary structure and are treated as random coils. Sequence pairs P<sub>3</sub>T<sub>3</sub> and P<sub>4</sub>T<sub>4</sub> contain 3 and 4 bp, respectively, in a hairpin-like stem on each strand. In addition to these complementary pairs, we also present kinetic data for the mismatched duplex, P<sub>4</sub>T<sub>3</sub>, which contains two terminal base pair mismatches (A·A and C·C).</p></sec><sec><title>Solution-phase studies</title><p>We qualitatively characterized the secondary structure of each single-stranded DNA (ssDNA) sequence designed for these studies by thermal melting. The UV absorbance of 2 μM ssDNA in 1, 0.5 and 0.1 M NaCl/TE buffer (TE: 10 mM Tris, pH 7.6 and 1 mM EDTA) was monitored at 260 nm while the temperature was ramped from 20 to 80°C at a rate of 0.5°C/min (Varian Cary 100 with a Peltier thermostatable multicell holder, temperature accuracy <±0.3°C). The duplex stability of each probe–target pair was also measured via thermal melting experiments in the same buffers; the temperature was ramped from 20 to 88°C at a slower rate of 0.25°C/min.</p><p>Kinetics of DNA hybridization was measured in three different ionic strength buffers: 1, 0.5 and 0.1 M NaCl/TE. Before hybridization, all target and probe molecules were separately annealed by rapidly heating each sequence to 80°C and slowly cooling to 20°C over an hour. Hybridization was then observed by monitoring the decrease in UV absorbance at 260 nm upon mixing equal molar concentrations of probe and target solutions. These solutions were mixed via hand pipetting or syringe injection into an empty 1 cm path-length semi-micro quartz cuvette. The cell was pre-equilibrated at 20°C and hybridization was monitored at this fixed temperature. The decrease in UV absorbance, caused by hypochromism that occurs during duplex formation, was monitored until there was no appreciable absorbance change over time. For hand mixing, the time required for pipetting the solutions into the cuvette and securing the instrument cover was ∼3 s; no kinetic data were collected during this time and the initial absorbance (at <italic>t</italic> = 0) was calculated based on the concentration and molecular extinction coefficients of the single strands mixed. For syringe injection, kinetic data were collected continuously, but reasonable UV absorbance values were not obtained until the injected solution volume reached the instrumental beam height in the cuvette. Time zero (<italic>t</italic> = 0) was assigned to this ‘reasonable’ point during the filling of the cuvette, although the uncertainty in this selection can be as much as ±1 s. Nevertheless, we have found that varying the choice of time zero over this temporal range of uncertainty does not affect the kinetic rate constants obtained from fitting. In addition, the different mixing methods have no influence on the kinetic data obtained, as is demonstrated for P<sub>0</sub>T<sub>0</sub> hybridization in 1 M NaCl/TE (Supplementary Figure S1).</p></sec><sec><title>Solution-phase kinetic analysis</title><p>The rate constants of solution-phase DNA hybridization were obtained by two different methods: linear and nonlinear second-order fits to the absorbance data. At time <italic>t</italic>, the concentration of ssDNA, <italic>C<sub>t</sub></italic>, is calculated using the following equation:
<disp-formula id="e1"><label>1</label><mml:math id="M1"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac><mml:mo>·</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
where <italic>A<sub>t</sub></italic> is the absorbance at time <italic>t</italic>, <italic>A</italic><sub>0</sub> is the absorbance of the ssDNA at <italic>t</italic> = 0, <italic>A</italic><sub>∞</sub> is the absorbance of the double-stranded DNA (dsDNA) at equilibrium and <italic>C</italic><sub>0</sub> is the initial concentration of ssDNA. Hybridization of equal molar probe and target single strands can be described by second-order reaction kinetics:
<disp-formula id="e2"><label>2</label><mml:math id="M2"><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>−</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>on</mml:mtext></mml:mrow></mml:msub><mml:mo>·</mml:mo><mml:mi>t</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
where <italic>k</italic><sub>on</sub> is the association rate constant. If we combine <xref ref-type="disp-formula" rid="e1">Equations 1</xref> and <xref ref-type="disp-formula" rid="e2">2</xref>, we find:
<disp-formula id="e3"><label>3</label><mml:math id="M3"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mi>∞</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>)</mml:mo><mml:mo>·</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>·</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mn>on</mml:mn></mml:mrow></mml:msub><mml:mo>·</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>·</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mn>on</mml:mn></mml:mrow></mml:msub><mml:mo>·</mml:mo><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
Dissociation rate constants are not considered in these equations because they are negligible for the conditions and sequences studied. As discussed below, all solution-phase hybridizations reach 100% completion. The rate constant, <italic>k</italic><sub>on</sub>, can be obtained by calculation of <italic>C<sub>t</sub></italic> and linear fitting (<xref ref-type="disp-formula" rid="e2">Equation 2</xref>) or by nonlinear fits to the raw experimental data (<xref ref-type="disp-formula" rid="e3">Equation 3</xref>). For data which follow a two-state model, values of <italic>k</italic><sub>on</sub> obtained by either of these two fitting methods agree within 10% error.</p></sec><sec><title>Surface studies</title><sec><title>Surface fabrication</title><p>The self-assembled DNA monolayers employed in all surface studies were fabricated according to a protocol developed previously in our laboratory (<xref ref-type="bibr" rid="b18">18</xref>). Briefly, the flat face of an SF-14 hemi-cylindrical prism was coated with ∼1 nm chromium and ∼50 nm gold after being cleaned with piranha solution (H<sub>2</sub>SO<sub>4</sub>:H<sub>2</sub>O<sub>2</sub> = 7:3) for 10 min,rinsed with copious amounts of distilled water and dried under nitrogen. Thiolated DNA probe molecules were deprotected and used immediately. To obtain the probe densities used in these studies (4.5–6.8 × 10<sup>12</sup> molecules/cm<sup>2</sup>), a solution of 0.5 μM probe in 1 M KH<sub>2</sub>PO<sub>4</sub> was injected into an all-Teflon flow cell sealed to the prism via o-ring and reacted for 4–5 h. This injection was followed by ∼50°C hot water rinse to remove non-specifically bound DNA probe molecules from the surface. The surface was then back-filled by exposure to 0.5 mM mercaptohexanol in 1 M KH<sub>2</sub>PO<sub>4</sub> for 5–6 h and rinsed with hot water again. After surface fabrication was complete, the surface was treated with 0.4% SDS (by weight in water) for 5 min and rinsed with distilled water.</p><p>All hybridization data presented in this study were obtained on surfaces with similar probe density (4.5–6.8 × 10<sup>12</sup> molecules/cm<sup>2</sup>). Because sequence content and secondary structure can affect the DNA probe coverage resulting from self assembly (<xref ref-type="bibr" rid="b19">19</xref>,<xref ref-type="bibr" rid="b20">20</xref>), the surface exposure time to both thiolated DNA probe and mercaptohexanol solutions was tuned in order to obtain probe densities in a narrow range.</p></sec></sec><sec><title>Hybridization and regeneration of the DNA probe surface</title><p>Surface hybridization experiments were performed under the same ionic strength conditions used in the solution-phase studies at room temperature (∼20°C). The probe surface was exposed to 1 μM ssDNA target strand in NaCl/TE buffer until equilibrium was attained. A control experiment, using non-complementary target, confirmed the absence of non-specific adsorption for each probe surface (data not shown). After hybridization, the probe surface (P<sub>0</sub>, P<sub>3</sub> or P<sub>4</sub>) was regenerated with 0.4% SDS and re-hybridized in various buffer solutions. We observed excellent reproducibility of hybridization kinetics and thermodynamics on the same surface, indicating the stability of probe films during experiments. Each probe surface could be SDS regenerated and re-hybridized >10 times.</p></sec><sec><title>SPR measurements</title><p>All surface DNA hybridization kinetic measurements were carried out via SPR spectroscopy. Detailed explanation of SPR theory, our experimental setup and data analysis methods have been given in earlier works (<xref ref-type="bibr" rid="b18">18</xref>,<xref ref-type="bibr" rid="b21">21</xref>,<xref ref-type="bibr" rid="b22">22</xref>). Briefly, we use a home-built SPR angle-scanning instrument to measure <italic>in situ</italic> reflectance from a gold-coated hemi-cylindrical prism at 632.8 nm. By fitting the obtained reflectivity profiles to a five-phase Fresnel optical model, we can obtain molecular surface coverage information. For the DNA submonolayers used in this study, probe and target coverages were determined by fixing the dielectric constant of the layer (ɛ<sub>layer</sub>) at a value of 2.0 (<xref ref-type="bibr" rid="b19">19</xref>). Angularly dependent light scattering and ellipsometry studies have reported differences in ɛ<sub>layer</sub> of 0.06–0.2 for ssDNA and dsDNA films (<xref ref-type="bibr" rid="b23">23</xref>,<xref ref-type="bibr" rid="b24">24</xref>). Our assumption of a single value of ɛ<sub>layer</sub> for all probes with varying degrees of secondary structure, therefore, can cause at most 3% error in our coverage calculations. The refractive index increment (d<italic>n</italic>/d<italic>c</italic>) values for each individual strand employed in these studies were determined based on previous refractometer measurements of individual nucleotides and used to calculate surface coverage (<xref ref-type="bibr" rid="b19">19</xref>). It was assumed that the d<italic>n</italic>/d<italic>c</italic> value for d<italic>G</italic>, although not measured, was similar to that of d<italic>A</italic>. Hybridization efficiencies were determined by taking the ratio of calculated target coverage to the immobilized probe coverage.</p></sec><sec><title>Analysis of surface kinetics</title><p>Observed hybridization rate constants were obtained by fitting hybridization efficiency data to the first-order Langmuir equation:
<disp-formula id="e4"><label>4</label><mml:math id="M4"><mml:mrow><mml:mi>Γ</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mi>Γ</mml:mi><mml:mrow><mml:mtext>max</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mtext>exp</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>eff</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mi>C</mml:mi><mml:mo>⋅</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
where Γ<sub>max</sub> is the maximal hybridization efficiency, <italic>k</italic><sub>eff</sub> is the effective rate constant for surface hybridization, and <italic>C</italic> is the target concentration (1 μM in this study). This equation assumes a homogeneous surface upon which all accessible binding sites are identical. In this work, dissociation rate constants are negligible (no target dissociation is observed during post-hybridization buffer rinse experiments) and therefore only one variable (<italic>k</italic><sub>eff</sub>) is considered in the fitting analysis for surface kinetic data. If the negligibly small dissociation rate constant was included as a second variable, then the resulting <italic>k</italic><sub>eff</sub> value obtained from fitting analysis would remain unchanged, although it would have a larger error.</p></sec></sec><sec><title>RESULTS AND DISCUSSION</title><sec><title>Secondary structure</title><p>In order to study the effects of ssDNA secondary structure on duplex formation, four sets of sequences were selected: P<sub>0</sub>T<sub>0</sub>, P<sub>3</sub>T<sub>3</sub>, P<sub>4</sub>T<sub>4</sub> and P<sub>4</sub>T<sub>3</sub> (<xref ref-type="table" rid="tbl1">Table 1</xref>). Each pair has a similar thermodynamic duplex stability but the number of base pairs involved in the individual ssDNA folded secondary structures varies. Duplex stability for each pair of sequences was confirmed by thermal melting experiments; all dsDNA pairs were found to have similar melting temperatures falling in a narrow range (Δ<italic>T</italic><sub>m</sub> < 2°C) (Supplementary Figure S2). This result rules out any stability effects on solution-phase and surface hybridization kinetics measured in this study, particularly for the P<sub>4</sub>T<sub>3</sub> duplex, which contains a 2 bp terminal mismatch. The terminal mismatch apparently has almost no effect on the thermodynamic duplex stability.</p><p>The secondary structure of each individual ssDNA sequence was qualitatively observed by thermal melting experiments (<xref ref-type="fig" rid="fig1">Figure 1</xref>). Only results in 1 M NaCl/TE are displayed, but the single strands behave similarly at all other ionic strengths studied (0.1 and 0.5 M, data not shown), exhibiting identical trends in absorbance change and melting profile. In general, as single-strand secondary structure increases, the absorbance change upon melting increases and the curve acquires a more sigmoidal shape. This shape appears as a result of the two states emerging in the strand at low and high temperatures: folded and unfolded, respectively. The magnitude of the absorbance change increases as both the number of base pairs unfolding and the hypochromicity of the strand increases.</p><p>The absorbance change that occurs over the temperature range measured for the P<sub>0</sub> and T<sub>0</sub> strands (left panel in <xref ref-type="fig" rid="fig1">Figure 1</xref>) is the result of base stacking. As the temperature increases, bases un-stack and the overall strand extinction coefficient increases. No sigmoidal shape is evident in these melting curves, indicating the absence of a folded state at low temperatures. The melting temperatures (<italic>T</italic><sub>m</sub>s) predicted by mFold for these strands under our solution conditions (denoted by the lines in <xref ref-type="fig" rid="fig1">Figure 1</xref>) also support a lack of secondary structure in these strands; the <italic>T</italic><sub>m</sub>s are at or below 20°C, indicating unfolded, random conformations for both P<sub>0</sub> and T<sub>0</sub>.</p><p>Other strand melting temperatures predicted by mFold agree qualitatively well with our experimental data. The vertical lines in <xref ref-type="fig" rid="fig1">Figure 1</xref> occur near the inflection points of the sigmoidal datasets obtained for P<sub>3</sub>, T<sub>3</sub>, P<sub>4</sub> and T<sub>4</sub>. <xref ref-type="scheme" rid="sch1">Scheme 1</xref> displays the general lowest energy structures predicted by mFold for these strands. Sequences P<sub>4</sub> and T<sub>4</sub> are capable of forming similar ‘hairpins’ having 4 bp in the stem, 10 bp in the loop and a 6 bp tail. These structures are very stable, having predicted <inline-formula><mml:math id="M5"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>G</mml:mi><mml:mn>20</mml:mn><mml:mo>°</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> values of −5.3 and −4.6 kcal/mol for P<sub>4</sub> and T<sub>4</sub>, respectively. Similarly, sequences P<sub>3</sub> and T<sub>3</sub> are capable of forming ‘hairpins’ with 3 bp in the stem, 5 bp in the loop and two tails containing 4 and 10 bp. These structures are slightly less stable, having predicted <inline-formula><mml:math id="M6"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>G</mml:mi><mml:mn>20</mml:mn><mml:mo>°</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> values of −3.1 and −3.8 kcal/mol for P<sub>3</sub> and T<sub>3</sub>, respectively.</p><p>Although sequences containing intramolecular hairpin structure, such as P<sub>4</sub> and T<sub>4</sub>, could form intermolecular dimers (P<sub>4</sub>P<sub>4</sub> and T<sub>4</sub>T<sub>4</sub>), for our experimental conditions (<xref ref-type="fig" rid="fig1">Figure 1</xref>), this is not the case. Concentration-dependent thermal melting studies of ssDNA and van't Hoff analysis (Supplementary Figure S3) indicate that 90% of P<sub>4</sub> strands and 100% of T<sub>4</sub> strands exist as hairpins, rather than dimers at 20°C and 1 μM ssDNA. Therefore, we confine our discussion in this work to hairpin secondary structure.</p></sec><sec><title>Solution-phase kinetic measurements</title><p>We find that the presence of secondary structure in the individual single DNA strands slows the process of DNA hybridization profoundly. <xref ref-type="fig" rid="fig2">Figure 2</xref> displays the solution-phase kinetics of duplex formation as monitored by UV absorbance spectroscopy and plotted in two different formats. A clear trend in the rate of absorbance change associated with hybridization is observed: P<sub>0</sub>T<sub>0</sub> > P<sub>3</sub>T<sub>3</sub> > P<sub>4</sub>T<sub>3</sub> > P<sub>4</sub>T<sub>4</sub>. Duplexes P<sub>0</sub>T<sub>0</sub>, P<sub>3</sub>T<sub>3</sub> and P<sub>4</sub>T<sub>3</sub> form completely within 5 min, while the duplex having the most secondary structure in its single strands, P<sub>4</sub>T<sub>4</sub>, requires 1 h for formation. Although the kinetic data displayed in <xref ref-type="fig" rid="fig2">Figure 2</xref> were measured in 0.5 M NaCl/TE, the same trend is observed for all other ionic strength buffers studied: 1 and 0.1 M NaCl/TE (Supplementary Figure S4).</p><p>Complete hybridization (100% efficiency) for all sequences was confirmed by thermally denaturing the duplexes immediately following single strand mixing and kinetic measurements. The same equilibrium absorbance value was re-established after slow strand annealing as was attained at ‘infinite time’ after room temperature mixing. For the hybridization of all sequences, the raw absorbance changes measured at room temperature scale well with the net number of base pairs formed during hybridization. For example, an absorbance change (Δ<italic>A</italic>) of 0.079 occurs during formation of the P<sub>0</sub>T<sub>0</sub> duplex, which corresponds to the formation of 25 bp. However, the P<sub>4</sub>T<sub>4</sub> individual single strands contain a total of eight pre-formed base pairs when mixed. As a result, a smaller Δ<italic>A</italic> of 0.053 is observed upon strand mixing that corresponds to the formation of an additional 17 bp during complete hybridization. This change in absorbance agrees closely with the theoretical value of 0.054 predicted from the P<sub>0</sub>T<sub>0</sub> results for a net formation of 17 bp.</p><p>In order to obtain quantitative kinetic information about the effects of secondary structure on DNA hybridization, we fit the data in <xref ref-type="fig" rid="fig2">Figure 2A and B</xref> to <xref ref-type="disp-formula" rid="e3">Equations 3</xref> and <xref ref-type="disp-formula" rid="e2">2</xref>, respectively. Interestingly, the data for duplexes P<sub>0</sub>T<sub>0</sub>, P<sub>3</sub>T<sub>3</sub> and P<sub>4</sub>T<sub>3</sub>, can be fit with a two-state model, whereas the P<sub>4</sub>T<sub>4</sub> hybridization data cannot. Indeed, P<sub>4</sub>T<sub>4</sub> (<xref ref-type="fig" rid="fig2">Figure 2B</xref>) requires two lines with different slopes to describe the duplex formation process. A simple two-state model is not appropriate for describing the hybridization of individual strands containing very stable intramolecular secondary structure, such as P<sub>4</sub>T<sub>4</sub>.</p><p>Rather, we propose that the two kinetic regimes measured for P<sub>4</sub>T<sub>4</sub> can be explained by nucleation and zippering. According to <xref ref-type="scheme" rid="sch1">Scheme 1</xref>, both P<sub>4</sub> and T<sub>4</sub> exist as hairpins, each with a 6 bp tail. The fast kinetic regime shown in <xref ref-type="fig" rid="fig2">Figure 2B</xref> may be the result of these tails nucleating or of their loops ‘kissing’, forming a partially hybridized species. The slow kinetic regime could then be caused by zippering of the remaining base pairs. This step is rate limiting because of the competition between intramolecular and intermolecular base pair formation. A slow displacement of the intramolecular base pairs in the hairpin stem must occur as the intermolecular base pairs are formed. Full-strand displacement of short oligomers has been measured by gel shift assay and shown to require hours for completion (<xref ref-type="bibr" rid="b25">25</xref>). Fluorescence correlation spectroscopy studies have also shown that spontaneous hairpin folding and unfolding in solution occurs in microseconds (<xref ref-type="bibr" rid="b26">26</xref>,<xref ref-type="bibr" rid="b27">27</xref>), indicating that our hybridization reactions are not limited by such a dissociative mechanistic step or pathway. In addition, the closed forms of the P<sub>4</sub> and T<sub>4</sub> strands are most likely favored under the room temperature, high-salt (>25 mM) conditions of our studies (<xref ref-type="bibr" rid="b28">28</xref>).</p><p><xref ref-type="table" rid="tbl2">Table 2</xref> lists the association rate constants determined from solution-phase and surface measurements in 0.5 M NaCl/TE. The surface association rate constants are discussed in the next section. For all four duplexes listed in the left panel of <xref ref-type="table" rid="tbl2">Table 2</xref>, the solution rate constants were obtained from fits to <xref ref-type="disp-formula" rid="e2">Equation 2</xref>, assuming that the entire absorbance change observed over time is caused by the formation of a full duplex (25 bp). For P<sub>4</sub>T<sub>4</sub>, a single rate constant cannot account for the data and values are provided for both the fast and slow kinetic regime.</p><p>For the fast kinetic regime, if we assume that the observed absorbance change is caused by the formation of a six nucleation base pair tail rather than all 25 bp and calculate a rate constant based on <xref ref-type="disp-formula" rid="e2">Equation 2</xref>, we find <italic>k</italic><sub>on</sub> = (12.5 ± 0.4) × 10<sup>5</sup> M<sup>−1</sup> s<sup>−1</sup>. This value agrees with the association rate constant measured for the probe–target pair devoid of any secondary structure, P<sub>0</sub>T<sub>0</sub>. This supports our proposed mechanism of tail nucleation followed by strand displacement for P<sub>4</sub>T<sub>4</sub> during the fast kinetic regime.</p></sec><sec><title>Surface kinetic measurements</title><p>The trend observed for hybridization rates in solution is also observed for target hybridization to surface-immobilized probe ssDNA at all ionic strengths studied. Surface hybridization data measured in 0.5 M NaCl/TE are plotted in <xref ref-type="fig" rid="fig3">Figure 3</xref> (for other ionic strength data see Supplementary Figure S5). Duplex P<sub>0</sub>T<sub>0</sub> forms the fastest, reaching equilibrium in 3 min, while P<sub>4</sub>T<sub>4</sub> is undoubtedly the slowest, requiring hours for complete duplex formation. This kinetic trend in rate constants, P<sub>0</sub>T<sub>0</sub> > P<sub>3</sub>T<sub>3</sub> > P<sub>4</sub>T<sub>3</sub> > P<sub>4</sub>T<sub>4</sub>, is clearly displayed by the normalized data presented in the inset of <xref ref-type="fig" rid="fig3">Figure 3</xref>. Given the results in solution, this trend is reasonable. However, there are results in the literature that suggest probe and target secondary structure do not affect surface hybridization rate (<xref ref-type="bibr" rid="b16">16</xref>).</p><p>We do, nevertheless, find significant differences between solution and surface hybridization kinetics, discussed below, and hybridization thermodynamics. Solution-phase hybridizations are able to achieve 100% hybridization efficiency or completion given equal molar quantities of probe and target, while surface hybridizations reach only 15–25% efficiency under conditions of target saturation. This is most probably a consequence of the steric and electrostatic hindrance caused by the confinement of ssDNA on the surface; a large percentage of probe is not target accessible. Duplexes P<sub>0</sub>T<sub>0</sub>, P<sub>3</sub>T<sub>3</sub> and P<sub>4</sub>T<sub>3</sub> also achieve the same efficiency within our ∼7% coverage calculation error associated with assumption of an isotropic refractive index for DNA (<xref ref-type="bibr" rid="b19">19</xref>) and our surface-to-surface variation of 8–9%. Duplex P<sub>4</sub>T<sub>4</sub>, however, only attains 15% efficiency after 30 min. Secondary structure clearly imposes some additional thermodynamic barrier to hybridization, which is particularly dominant at low ionic strengths (Supplementary Figure S5C).</p><p>Secondary structure effects on surface hybridization kinetics are quantitated by fitting the measured data to a traditional Langmuir model, <xref ref-type="disp-formula" rid="e4">Equation 4</xref>. Effective association rate constants, determined by fitting the first 30 minutes of hybridization data, are listed in the right panel of Table 2. Values obtained are independent of probe density, as we limited the surfaces studied to a narrow density range, 4.5–6.8 × 1012 molecules/cm<sup>2</sup>. We have shown previously that kinetics can vary over wide ranges of probe density, but remain virtually unaffected by densities in narrow or similar regimes (<xref ref-type="bibr" rid="b29">29</xref>).</p><p>As secondary structure increases, the uncertainty (error) obtained from fitting the data to a Langmuir model beyond 30 min increases. For P<sub>0</sub>T<sub>0</sub>, the error associated with the hybridization rate constant is 5–7% for all time scales fit, whereas the error obtained from fitting P<sub>4</sub>T<sub>3</sub> hybridization is 30% on long time scales (2 h). The Langmuir model, however, completely fails to fit the P<sub>4</sub>T<sub>4</sub> data beyond 30 min; the hybridization process is very slow and does not follow a simple two-state physical mechanism (for data fits see Supplementary Figure S5). Another model, such as that used to describe hybridization to structured probes containing G-quartets (<xref ref-type="bibr" rid="b29">29</xref>,<xref ref-type="bibr" rid="b30">30</xref>), could be applied to the P<sub>4</sub>T<sub>4</sub> system. Additional fitting parameters needed to describe the rates of folding and unfolding of the probe may add uncertainty. This model was found to predict faster hybridization rates for probes containing secondary structure compared to ‘random’ sequences, in contrast to our observed trend. Clearly better models are needed to describe the surface data, perhaps including site interactions.</p></sec><sec><title>Comparison of surface and solution-phase results</title><p>DNA hybridization has been studied extensively in bulk solution and on a variety of solid supports using a number of different experimental techniques and conditions. Because of differences in ionic strength, pH, strand sequence and concentration, temperature, and buffer additives, it is often difficult to compare measurements of hybridization in solution and on the surface. It is known that the solid support affects DNA hybridization on surfaces (<xref ref-type="bibr" rid="b31">31</xref>), but few studies have attempted to systematically quantify this effect. The lack of <italic>in situ</italic> experimental comparative data makes it difficult to predict the performance of surface biosensors from calculated or observed solution-phase behavior.</p><p>Here, we have systematically studied the kinetics of DNA hybridization in both surface and solution-phase environments. Of course, our comparison is based on measurements from two techniques monitoring different events: solution-phase UV absorbance measurements probing base pair formation and SPR measurements indirectly probing ‘target recognition’. Recent work (<xref ref-type="bibr" rid="b32">32</xref>) suggests that surface analytical methods such as QCM and SPR do not detect complete duplex hybridization, but instead, detect duplex nucleation or ‘initial target recognition’. Their voltammetry studies indicate that complete zippering of the duplex on the surface requires hours instead of the mere minutes measured under the same conditions by QCM. Nevertheless, it has long been accepted that the rate-limiting step in solution-phase DNA hybridization of short strands such as those studied here is nucleation (<xref ref-type="bibr" rid="b33">33</xref>). As a result, solution-phase hybridization rates reflecting nucleation or some combination of nucleation and displacement, are comparable to SPR measurements.</p><p>For each of our sequence pairs, the associative kinetics of surface DNA hybridization are suppressed by a factor of 20- to 40-fold compared to solution-phase hybridization (<xref ref-type="table" rid="tbl2">Table 2</xref>). This result compares favorably with the 5- to 10-fold suppression in hybridization rates of 22mers observed with FRET on microparticles (<xref ref-type="bibr" rid="b34">34</xref>). In general, surface suppression is likely caused by steric and electrostatic hindrance present in the DNA probe film as well as conformational restriction of the surface-tethered strands. As a result, the surface kinetic suppression factor we have determined for thiolated DNA immobilized on gold will likely be affected by changes in probe attachment and density. Based on previous studies (<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b32">32</xref>,<xref ref-type="bibr" rid="b35">35</xref>), we predict that DNA hybridization rates will increase at lower probe densities and for probe films containing spacers, but it is not clear at this time whether any measurable, biosensor-relevant condition exists for which solution and surface hybridization rates agree.</p><p>We have also observed that secondary structure present in the individual DNA single strands suppresses the DNA hybridization kinetics in both the surface and solution-phase environments. <xref ref-type="fig" rid="fig4">Figure 4</xref> displays this suppression with a plot of measured solution and surface associative rate constants versus the degree of secondary structure in the duplex-forming probe and target strands (combined <inline-formula><mml:math id="M7"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>G</mml:mi><mml:mn>20</mml:mn><mml:mo>°</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> values calculated from mFold for each strand). The measured hybridization rate constants in solution and on the surface have a similar linear relationship with the stability of secondary structure when scaled. A previous solution–surface comparison (<xref ref-type="bibr" rid="b16">16</xref>) also reported a secondary structure trend in hybridization kinetics for a series of designed hairpins, but only in solution. No dependence on secondary structure was observed for fluorescence-based surface studies with identical sequences. This may have been caused by excessive probe loss during the <italic>ex situ</italic> rinsing of the probe-modified beads employed or by probe-surface fluorophore quenching.</p><p>The data in <xref ref-type="fig" rid="fig4">Figure 4</xref> suggest that adding three intramolecular base pairs to the probe and target strands involved in duplex formation (∼−6 kcal/mol combined stability) causes a 2-fold decrease in hybridization rate both in solution and on the surface. This exact factor could change slightly depending on the sequence composition, length or structure selected in the probe design process. In general, adding a G·C rather than an A·T base pair to the stem causes greater hairpin stability and could decrease the hybridization kinetics more profoundly. The size and rigidity of the hairpin loop have been shown to affect thermodynamic stability (<xref ref-type="bibr" rid="b26">26</xref>,<xref ref-type="bibr" rid="b36">36</xref>,<xref ref-type="bibr" rid="b37">37</xref>) and could also affect duplex formation rates. In addition, the length of hairpin ‘tails’, which can be sites for duplex nucleation according to our proposed hybridization mechanism, may be important to kinetic rates. Nevertheless, we have provided a general relationship between the stability of secondary structure in the individual strands involved and the resultant hybridization kinetics. Although they are suppressed, the DNA hybridization rates observed on the surface mirror those measured in solution. This finding may have implications for the selection of experimental conditions and probe sequences used in conjunction with surface-based biosensors.</p></sec></sec><sec><title>CONCLUSIONS</title><p>We have shown that probe and target secondary structure affect the DNA hybridization kinetics both in solution and on the surface. Although the planar gold surface and probe layer environment suppress the measured rates 20- to 40-fold, the effects of secondary structure are similar in solution and surface environments. We have provided a general correlation between probe and target intramolecular structures predicted by computational algorithms such as mFold and the hybridization kinetics observed for these species. These results may be applied to ongoing work in our lab on aptamer-based biosensors and, more generally, to probe design for other DNA-based sensors.</p></sec><sec><title>SUPPLEMENTARY DATA</title><p>Supplementary Data are available at NAR online.</p></sec>
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</body><back><ack><p>We acknowledge fruitful discussions with Lucian Postelnicu at Boston University. This work is supported by the National Cancer Institute of the NIH (CA 89562) and the National Science Foundation (DBI-0096731). This work was partially supported by the Army Research Laboratory (Cooperative Agreement DAAD19-00-2-0004) and resources at the Boston University Photonics Center. Funding to pay the Open Access publication charges for this article was provided by the NIH and the Department of Chemistry, Boston University.</p><p><italic>Conflict of interest statement.</italic> None declared.</p></ack><ref-list><title>REFERENCES</title><ref id="b1"><label>1</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Okahata</surname><given-names>Y.</given-names></name><name><surname>Kawase</surname><given-names>M.</given-names></name><name><surname>Niikura</surname><given-names>K.</given-names></name><name><surname>Ohtake</surname><given-names>F.</given-names></name><name><surname>Furusawa</surname><given-names>H.</given-names></name><name><surname>Ebara</surname><given-names>Y.</given-names></name></person-group><article-title>Kinetic measurements of DNA hybridisation an oligonucleotide-immobilized 27-MHz quartz crystal microbalance</article-title><source>Anal. Chem.</source><year>1998</year><volume>70</volume><fpage>1288</fpage><lpage>1296</lpage><pub-id pub-id-type="pmid">15779144</pub-id></citation></ref><ref id="b2"><label>2</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Xu</surname><given-names>J.</given-names></name><name><surname>Craig</surname><given-names>S.L.</given-names></name></person-group><article-title>Thermodynamics of DNA hybridization on gold nanoparticles</article-title><source>J. Am. Chem. Soc.</source><year>2005</year><volume>127</volume><fpage>13227</fpage><lpage>13231</lpage><pub-id pub-id-type="pmid">16173751</pub-id></citation></ref><ref id="b3"><label>3</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Wetmur</surname><given-names>J.G.</given-names></name><name><surname>Davidson</surname><given-names>N.</given-names></name></person-group><article-title>Kinetics of renaturation of DNA</article-title><source>J. Mol. Biol.</source><year>1968</year><volume>31</volume><fpage>349</fpage><lpage>370</lpage><pub-id pub-id-type="pmid">5637197</pub-id></citation></ref><ref id="b4"><label>4</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Morrison</surname><given-names>L.E.</given-names></name><name><surname>Stols</surname><given-names>L.M.</given-names></name></person-group><article-title>Sensitive fluorescence-based thermodynamic and kinetic measurements of DNA hybridization in solution</article-title><source>Biochemistry</source><year>1993</year><volume>32</volume><fpage>3095</fpage><lpage>3104</lpage><pub-id pub-id-type="pmid">8457571</pub-id></citation></ref><ref id="b5"><label>5</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>SantaLucia</surname><given-names>J.</given-names></name></person-group><article-title>A unified view of polymer, dumbbell, and oligonucleotide DNA nearest-neighbor thermodynamics</article-title><source>Proc. Natl Acad. Sci. USA</source><year>1998</year><volume>95</volume><fpage>1460</fpage><lpage>1465</lpage><pub-id pub-id-type="pmid">9465037</pub-id></citation></ref><ref id="b6"><label>6</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Peyret</surname><given-names>N.</given-names></name><name><surname>Seneviratne</surname><given-names>P.A.</given-names></name><name><surname>Allawi</surname><given-names>H.T.</given-names></name><name><surname>SantaLucia</surname><given-names>J.</given-names></name></person-group><article-title>Nearest-neighbor thermodynamics and NMR of DNA sequences with internal A·A, C·C, G·G and T·T mismatches</article-title><source>Biochemistry</source><year>1999</year><volume>38</volume><fpage>3468</fpage><lpage>3477</lpage><pub-id pub-id-type="pmid">10090733</pub-id></citation></ref><ref id="b7"><label>7</label><citation citation-type="book"><person-group person-group-type="author"><name><surname>Peyret</surname><given-names>N.</given-names></name></person-group><article-title>Prediction of nucleic acid hybridization: parameters and algorithms</article-title><year>2000</year><publisher-loc>Detroit, MI</publisher-loc><publisher-name>Wayne State University</publisher-name><comment>PhD Dissertation</comment></citation></ref><ref id="b8"><label>8</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Zuker</surname><given-names>M.</given-names></name></person-group><article-title>Mfold web server for nucleic acid folding and hybridization prediction</article-title><source>Nucleic Acids Res.</source><year>2003</year><volume>31</volume><fpage>3406</fpage><lpage>3415</lpage><pub-id pub-id-type="pmid">12824337</pub-id></citation></ref><ref id="b9"><label>9</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Holbrook</surname><given-names>J.A.</given-names></name><name><surname>Capp</surname><given-names>M.W.</given-names></name><name><surname>Saecker</surname><given-names>R.M.</given-names></name><name><surname>Record</surname><given-names>M.T.</given-names></name></person-group><article-title>Enthalpy and heat capacity changes for formation of an oligomeric DNA duplex: interpretation in terms of coupled processes of formation and association of single-stranded helices</article-title><source>Biochemistry</source><year>1999</year><volume>38</volume><fpage>8409</fpage><lpage>8422</lpage><pub-id pub-id-type="pmid">10387087</pub-id></citation></ref><ref id="b10"><label>10</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Studier</surname><given-names>F.W.</given-names></name></person-group><article-title>Effects of conformation of single-stranded DNA on renaturation and aggregation</article-title><source>J. Mol. Biol.</source><year>1969</year><volume>41</volume><fpage>199</fpage><lpage>209</lpage><pub-id pub-id-type="pmid">5801474</pub-id></citation></ref><ref id="b11"><label>11</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Lima</surname><given-names>W.F.</given-names></name><name><surname>Monia</surname><given-names>B.P.</given-names></name><name><surname>Ecker</surname><given-names>D.J.</given-names></name><name><surname>Freier</surname><given-names>S.M.</given-names></name></person-group><article-title>Implication of RNA structure on antisense oligonucleotide hybridization kinetics</article-title><source>Biochemistry</source><year>1992</year><volume>31</volume><fpage>12055</fpage><lpage>12061</lpage><pub-id pub-id-type="pmid">1280997</pub-id></citation></ref><ref id="b12"><label>12</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Schwille</surname><given-names>P.</given-names></name><name><surname>Oehlenschlager</surname><given-names>F.</given-names></name><name><surname>Walter</surname><given-names>N.G.</given-names></name></person-group><article-title>Quantitative hybridization kinetics of DNA probes to RNA in solution followed by diffusional fluorescence correlation analysis</article-title><source>Biochemistry</source><year>1996</year><volume>35</volume><fpage>10182</fpage><lpage>10193</lpage><pub-id pub-id-type="pmid">8756483</pub-id></citation></ref><ref id="b13"><label>13</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Vesnaver</surname><given-names>G.</given-names></name><name><surname>Breslauer</surname><given-names>K.J.</given-names></name></person-group><article-title>The contribution of DNA single-stranded order to the thermodynamics of duplex formation</article-title><source>Proc. Natl Acad. Sci. USA</source><year>1991</year><volume>88</volume><fpage>3569</fpage><lpage>3573</lpage><pub-id pub-id-type="pmid">2023903</pub-id></citation></ref><ref id="b14"><label>14</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Kushon</surname><given-names>S.A.</given-names></name><name><surname>Jordan</surname><given-names>J.P.</given-names></name><name><surname>Seifert</surname><given-names>J.L.</given-names></name><name><surname>Nielsen</surname><given-names>H.</given-names></name><name><surname>Nielsen</surname><given-names>P.E.</given-names></name><name><surname>Armitage</surname><given-names>B.A.</given-names></name></person-group><article-title>Effect of secondary structure on the thermodynamics and kinetics of PNA hybridization to DNA hairpins</article-title><source>J. Am. Chem. Soc.</source><year>2001</year><volume>123</volume><fpage>10805</fpage><lpage>10813</lpage><pub-id pub-id-type="pmid">11686681</pub-id></citation></ref><ref id="b15"><label>15</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Bonnet</surname><given-names>G.</given-names></name><name><surname>Tyagi</surname><given-names>S.</given-names></name><name><surname>Libchaber</surname><given-names>A.</given-names></name><name><surname>Kramer</surname><given-names>F.R.</given-names></name></person-group><article-title>Thermodynamic basis of the enhanced specificity of structured DNA probes</article-title><source>Proc. Natl Acad. Sci. USA</source><year>1999</year><volume>96</volume><fpage>6171</fpage><lpage>6176</lpage><pub-id pub-id-type="pmid">10339560</pub-id></citation></ref><ref id="b16"><label>16</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Sekar</surname><given-names>M.M.A.</given-names></name><name><surname>Bloch</surname><given-names>W.</given-names></name><name><surname>St John</surname><given-names>P.M.</given-names></name></person-group><article-title>Comparative study of sequence-dependent hybridization kinetics in solution and on microspheres</article-title><source>Nucleic Acids Res.</source><year>2005</year><volume>33</volume><fpage>366</fpage><lpage>375</lpage><pub-id pub-id-type="pmid">15653637</pub-id></citation></ref><ref id="b17"><label>17</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Chien</surname><given-names>F.C.</given-names></name><name><surname>Liu</surname><given-names>J.S.</given-names></name><name><surname>Su</surname><given-names>H.J.</given-names></name><name><surname>Kao</surname><given-names>L.A.</given-names></name><name><surname>Chiou</surname><given-names>C.F.</given-names></name><name><surname>Chen</surname><given-names>W.Y.</given-names></name><name><surname>Chen</surname><given-names>S.J.</given-names></name></person-group><article-title>An investigation into the influence of secondary structures on DNA hybridization using surface plasmon resonance biosensing</article-title><source>Chem. Phys. Lett.</source><year>2004</year><volume>397</volume><fpage>429</fpage><lpage>434</lpage></citation></ref><ref id="b18"><label>18</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Peterlinz</surname><given-names>K.A.</given-names></name><name><surname>Georgiadis</surname><given-names>R.M.</given-names></name><name><surname>Herne</surname><given-names>T.M.</given-names></name><name><surname>Tarlov</surname><given-names>M.J.</given-names></name></person-group><article-title>Observation of hybridization and dehybridization of thiol-tethered DNA using two-color surface plasmon resonance spectroscopy</article-title><source>J. Am. Chem. Soc.</source><year>1997</year><volume>119</volume><fpage>3401</fpage><lpage>3402</lpage></citation></ref><ref id="b19"><label>19</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Wolf</surname><given-names>L.K.</given-names></name><name><surname>Gao</surname><given-names>Y.</given-names></name><name><surname>Georgiadis</surname><given-names>R.M.</given-names></name></person-group><article-title>Sequence-dependent DNA immobilization: specific versus nonspecific contributions</article-title><source>Langmuir</source><year>2004</year><volume>20</volume><fpage>3357</fpage><lpage>3361</lpage><pub-id pub-id-type="pmid">15875869</pub-id></citation></ref><ref id="b20"><label>20</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Steichen</surname><given-names>M.</given-names></name><name><surname>Buess-Herman</surname><given-names>C.</given-names></name></person-group><article-title>Electrochemical detection of the immobilization and hybridization of unlabeled linear and hairpin DNA on gold</article-title><source>Electrochem. Commun.</source><year>2005</year><volume>7</volume><fpage>416</fpage><lpage>420</lpage></citation></ref><ref id="b21"><label>21</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Peterlinz</surname><given-names>K.A.</given-names></name><name><surname>Georgiadis</surname><given-names>R.M.</given-names></name></person-group><article-title><italic>In situ</italic> kinetics of self-assembly by surface plasmon resonance spectroscopy</article-title><source>Langmuir</source><year>1996</year><volume>12</volume><fpage>4731</fpage><lpage>4740</lpage></citation></ref><ref id="b22"><label>22</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Georgiadis</surname><given-names>R.M.</given-names></name><name><surname>Peterlinz</surname><given-names>K.A.</given-names></name><name><surname>Peterson</surname><given-names>A.W.</given-names></name></person-group><article-title>Quantitative measurements and modeling of kinetics in nucleic acid monolayer films using SPR spectroscopy</article-title><source>J. Am. Chem. Soc.</source><year>2000</year><volume>122</volume><fpage>3166</fpage><lpage>3173</lpage></citation></ref><ref id="b23"><label>23</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Elhadj</surname><given-names>S.</given-names></name><name><surname>Singh</surname><given-names>G.</given-names></name><name><surname>Saraf</surname><given-names>R.F.</given-names></name></person-group><article-title>Optical properties of an immobilized DNA monolayer from 255 to 700 nm</article-title><source>Langmuir</source><year>2004</year><volume>20</volume><fpage>5539</fpage><lpage>5543</lpage><pub-id pub-id-type="pmid">15986697</pub-id></citation></ref><ref id="b24"><label>24</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Henke</surname><given-names>L.</given-names></name><name><surname>Piunno</surname><given-names>P.A.E.</given-names></name><name><surname>Nagy</surname><given-names>N.</given-names></name><name><surname>Wust</surname><given-names>C.C.</given-names></name><name><surname>Krull</surname><given-names>U.J.</given-names></name></person-group><article-title>Rapid and simple technique for the determination of the refractive index of ultra-thin organic films on planar transparent substrates using forward light scatter</article-title><source>Anal. Chim. Acta</source><year>2001</year><volume>433</volume><fpage>31</fpage><lpage>45</lpage></citation></ref><ref id="b25"><label>25</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Reynaldo</surname><given-names>L.P.</given-names></name><name><surname>Vologodskii</surname><given-names>A.V.</given-names></name><name><surname>Neri</surname><given-names>B.P.</given-names></name><name><surname>Lyamichev</surname><given-names>V.I.</given-names></name></person-group><article-title>The kinetics of oligonucleotide replacements</article-title><source>J. Mol. Biol.</source><year>2000</year><volume>297</volume><fpage>511</fpage><lpage>520</lpage><pub-id pub-id-type="pmid">10715217</pub-id></citation></ref><ref id="b26"><label>26</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Jung</surname><given-names>J.M.</given-names></name><name><surname>Van Orden</surname><given-names>A.</given-names></name></person-group><article-title>Folding and unfolding kinetics of DNA hairpins in flowing solution by multiparameter fluorescence correlation spectroscopy</article-title><source>J. Phys. Chem. B</source><year>2005</year><volume>109</volume><fpage>3648</fpage><lpage>3657</lpage></citation></ref><ref id="b27"><label>27</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Bonnet</surname><given-names>G.</given-names></name><name><surname>Krichevsky</surname><given-names>O.</given-names></name><name><surname>Libchaber</surname><given-names>A.</given-names></name></person-group><article-title>Kinetics of conformational fluctuations in DNA hairpin-loops</article-title><source>Proc. Natl Acad. Sci. USA</source><year>1998</year><volume>95</volume><fpage>8602</fpage><lpage>8606</lpage><pub-id pub-id-type="pmid">9671724</pub-id></citation></ref><ref id="b28"><label>28</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Jung</surname><given-names>J.M.</given-names></name><name><surname>Van Orden</surname><given-names>A.</given-names></name></person-group><article-title>A three-state mechanism for DNA hairpin folding characterized by multiparameter fluorescence fluctuation spectroscopy</article-title><source>J. Am. Chem. Soc.</source><year>2006</year><volume>128</volume><fpage>1240</fpage><lpage>1249</lpage><pub-id pub-id-type="pmid">16433541</pub-id></citation></ref><ref id="b29"><label>29</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Zhao</surname><given-names>Y.</given-names></name><name><surname>Kan</surname><given-names>Z.Y.</given-names></name><name><surname>Zeng</surname><given-names>Z.X.</given-names></name><name><surname>Hao</surname><given-names>Y.H.</given-names></name><name><surname>Chen</surname><given-names>H.</given-names></name><name><surname>Tan</surname><given-names>Z.</given-names></name></person-group><article-title>Determining the folding and unfolding rate constants of nucleic acids by biosensor. Application to telomere G-quadruplex</article-title><source>J. Am. Chem. Soc.</source><year>2004</year><volume>126</volume><fpage>13255</fpage><lpage>13264</lpage><pub-id pub-id-type="pmid">15479079</pub-id></citation></ref><ref id="b30"><label>30</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Halder</surname><given-names>K.</given-names></name><name><surname>Chowdhury</surname><given-names>S.</given-names></name></person-group><article-title>Kinetic resolution of bimolecular hybridization versus intramolecular folding in nucleic acids by surface plasmon resonance: application to G-quadruplex/duplex competition in human c-myc promoter</article-title><source>Nucleic Acids Res.</source><year>2005</year><volume>33</volume><fpage>4466</fpage><lpage>4474</lpage><pub-id pub-id-type="pmid">16085756</pub-id></citation></ref><ref id="b31"><label>31</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Levicky</surname><given-names>R.</given-names></name><name><surname>Horgan</surname><given-names>A.</given-names></name></person-group><article-title>Physicochemical perspectives on DNA microarray and biosensor technologies</article-title><source>Trends Biotechnol.</source><year>2005</year><volume>23</volume><fpage>143</fpage><lpage>149</lpage><pub-id pub-id-type="pmid">15734557</pub-id></citation></ref><ref id="b32"><label>32</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Wong</surname><given-names>E.L.S.</given-names></name><name><surname>Chow</surname><given-names>E.</given-names></name><name><surname>Gooding</surname><given-names>J.J.</given-names></name></person-group><article-title>DNA recognition interfaces: the influence of interfacial design on the efficiency and kinetics of hybridization</article-title><source>Langmuir</source><year>2005</year><volume>21</volume><fpage>6957</fpage><lpage>6965</lpage><pub-id pub-id-type="pmid">16008409</pub-id></citation></ref><ref id="b33"><label>33</label><citation citation-type="book"><person-group person-group-type="author"><name><surname>Tinoco</surname><given-names>I.</given-names></name><name><surname>Crothers</surname><given-names>D.M.</given-names></name><name><surname>Bloomfield</surname><given-names>V.A.</given-names></name></person-group><source>Nucleic Acids: Structure, Properties and Functions</source><year>2000</year><publisher-loc>Sausalito, CA</publisher-loc><publisher-name>University Science Books</publisher-name><comment>Chapter 8</comment></citation></ref><ref id="b34"><label>34</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Henry</surname><given-names>M.R.</given-names></name><name><surname>Stevens</surname><given-names>P.W.</given-names></name><name><surname>Sun</surname><given-names>J.</given-names></name><name><surname>Kelso</surname><given-names>D.M.</given-names></name></person-group><article-title>Real-time measurements of DNA hybridization on microparticles with fluorescence resonance energy transfer</article-title><source>Anal. Biochem.</source><year>1999</year><volume>276</volume><fpage>204</fpage><lpage>214</lpage><pub-id pub-id-type="pmid">10603244</pub-id></citation></ref><ref id="b35"><label>35</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Peterson</surname><given-names>A.W.</given-names></name><name><surname>Heaton</surname><given-names>R.J.</given-names></name><name><surname>Georgiadis</surname><given-names>R.M.</given-names></name></person-group><article-title>The effect of surface probe density on DNA hybridization</article-title><source>Nucleic Acids Res.</source><year>2001</year><volume>29</volume><fpage>5163</fpage><lpage>5168</lpage><pub-id pub-id-type="pmid">11812850</pub-id></citation></ref><ref id="b36"><label>36</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Du</surname><given-names>H.</given-names></name><name><surname>Disney</surname><given-names>M.D.</given-names></name><name><surname>Miller</surname><given-names>B.L.</given-names></name><name><surname>Krauss</surname><given-names>T.D.</given-names></name></person-group><article-title>Hybridization-based unquenching of DNA hairpins on Au surfaces: prototypical ‘molecular beacon’ biosensors</article-title><source>J. Am. Chem. Soc.</source><year>2003</year><volume>125</volume><fpage>4012</fpage><lpage>4013</lpage><pub-id pub-id-type="pmid">12670198</pub-id></citation></ref><ref id="b37"><label>37</label><citation citation-type="journal"><person-group person-group-type="author"><name><surname>Du</surname><given-names>H.</given-names></name><name><surname>Strohsahl</surname><given-names>C.M.</given-names></name><name><surname>Camera</surname><given-names>J.</given-names></name><name><surname>Miller</surname><given-names>B.L.</given-names></name><name><surname>Krauss</surname><given-names>T.D.</given-names></name></person-group><article-title>Sensitivity and specificity of metal surface-immobilized ‘molecular beacon’ biosensors</article-title><source>J. Am. Chem. Soc.</source><year>2005</year><volume>127</volume><fpage>7932</fpage><lpage>7940</lpage><pub-id pub-id-type="pmid">15913384</pub-id></citation></ref></ref-list><sec sec-type="display-objects"><title>Figures and Tables</title><fig id="fig1" position="float"><label>Figure 1</label><caption><p>Thermal melting of ssDNA sequences monitored by UV absorbance spectroscopy. Sequences are listed in <xref ref-type="table" rid="tbl1">Table 1</xref>. Melting curves shown were collected at a ramp rate of 0.5°C/min for 2 μM ssDNA in 1 M NaCl/TE. Lines indicate the <italic>T</italic><sub>m</sub>s predicted by mFold for each sequence under these conditions.</p></caption><graphic xlink:href="gkl422f1"/></fig><fig id="sch1" position="float"><label>Scheme 1</label><caption><p>Depiction of the forms for the sequences, illustrating lowest energy structures as predicted by mFold under conditions of 2 μM strand concentration and 1 M ionic strength. Structures contain no loops, a 5 base loop with 3 bp in the stem, and a 10 base loop with 4 bp in the stem, respectively, from left to right.</p></caption><graphic xlink:href="gkl422s1"/></fig><fig id="fig2" position="float"><label>Figure 2</label><caption><p>Kinetics of DNA hybridization in solution. [Probe] = [Target] = 1 μM, <italic>T</italic> = 20°C, and [NaCl] = 0.5 M. (<bold>A</bold>) Normalized absorbance change upon injection or hand mixing of single strands as a function of time. The raw values of Δ<italic>A</italic> at ‘infinite time’ or equilibrium are 0.079, 0.063, 0.049 and 0.053 for P<sub>0</sub>T<sub>0</sub>, P<sub>3</sub>T<sub>3</sub>, P<sub>4</sub>T<sub>3</sub> and P<sub>4</sub>T<sub>4</sub>, respectively. These values generally scale with the net number of Watson–Crick base pairs formed during hybridization (for details see text). (<bold>B</bold>) Linearized absorbance data plotted as inverse concentration versus time. Solid lines are fits to the data and the slopes correspond to the second-order hybridization rate constant for each set of sequences. Mixing of P<sub>0</sub>T<sub>0</sub>, P<sub>3</sub>T<sub>3</sub> and P<sub>4</sub>T<sub>3</sub> was done by hand pipetting, while P<sub>4</sub>T<sub>4</sub> was carried out by syringe injection.</p></caption><graphic xlink:href="gkl422f2"/></fig><fig id="fig3" position="float"><label>Figure 3</label><caption><p>Surface hybridization kinetics. Hybridizations are monitored for many hours, but only shown on a 30 min time-scale here. Hybridization of duplexes P<sub>0</sub>T<sub>0</sub> and P<sub>3</sub>T<sub>3</sub> is very fast, while hybridization of P<sub>4</sub>T<sub>4</sub> is very slow. Duplex P<sub>4</sub>T<sub>4</sub> reaches 20% hybridization efficiency, but only after overnight target exposure. For all hybridizations, [Target] = 1 μM, T = 20°C, and [NaCl] = 0.5 M. Exposure of each probe surface to control target strands yields no significant binding (data not shown). Probe densities are 4.5 × 10<sup>12</sup>, 6.8 × 10<sup>12</sup> and 5.7 × 10<sup>12</sup> molecules/cm<sup>2</sup> for P<sub>0</sub>, P<sub>3</sub> and P<sub>4</sub> probe surfaces, respectively. (Inset) Hybridizations normalized at 30 min for comparison of kinetic rates.</p></caption><graphic xlink:href="gkl422f3"/></fig><fig id="fig4" position="float"><label>Figure 4</label><caption><p>Comparison of <italic>k</italic><sub>eff</sub> (left axis, closed diamond) and <italic>k</italic><sub>on</sub> (right axis, open diamond) versus <inline-formula><mml:math id="M8"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>G</mml:mi><mml:mn>20</mml:mn><mml:mo>°</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> of ssDNA folding in bulk solution and on the surface, respectively. Plotted values of <inline-formula><mml:math id="M9"><mml:mrow><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>G</mml:mi><mml:mn>20</mml:mn><mml:mo>°</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> for each single strand involved in the duplex were calculated by mFold and combined. Calculations with mFold were carried out under the same conditions employed in our experiments. The dotted line is a guide to the eye.</p></caption><graphic xlink:href="gkl422f4"/></fig><table-wrap id="tbl1" position="float"><label>Table 1</label><caption><p>Oligonucleotide sequences and nomenclature</p></caption><table frame="hsides" rules="groups"><tbody><tr><td colspan="2" align="left" rowspan="1">Probe</td></tr><tr><td align="left" colspan="1" rowspan="1">P<sub>0</sub></td><td align="left" colspan="1" rowspan="1">5′-GTTGTCAAGATGCTACCGTTCAGAG-3′</td></tr><tr><td align="left" colspan="1" rowspan="1">P<sub>3</sub></td><td align="left" colspan="1" rowspan="1">5′-AGAT<underline>CAG</underline>TGCGT<underline>CTG</underline>TACTAGCAGT-3′</td></tr><tr><td align="left" colspan="1" rowspan="1">P<sub>4</sub></td><td align="left" colspan="1" rowspan="1">5′-AGATCA<underline>GTGC</underline>GTCTGTACTA<underline>GCAC</underline>A-3′</td></tr><tr><td colspan="2" align="left" rowspan="1">Target (complementary to the corresponding probe)</td></tr><tr><td align="left" colspan="1" rowspan="1">T<sub>0</sub></td><td align="left" colspan="1" rowspan="1">5′-CTCTGAACGGTAGCATCTTGACAAC-3′</td></tr><tr><td align="left" colspan="1" rowspan="1">T<sub>3</sub></td><td align="left" colspan="1" rowspan="1">5′-ACTGCTAGTA<underline>CAG</underline>ACGCA<underline>CTG</underline>ATCT-3′</td></tr><tr><td align="left" colspan="1" rowspan="1">T<sub>4</sub></td><td align="left" colspan="1" rowspan="1">5′-T<underline>GTGC</underline>TAGTACAGAC<underline>GCAC</underline>TGATCT-3′</td></tr></tbody></table></table-wrap><table-wrap id="tbl2" position="float"><label>Table 2</label><caption><p>Association DNA hybridization rate constants determined from solution-phase and surface measurements in 0.5 M NaCl/TE</p></caption><table frame="hsides" rules="groups"><thead><tr><th align="left" colspan="1" rowspan="1">Sequence</th><th colspan="2" align="left" rowspan="1"><italic>k</italic> (10<sup>5</sup> M<sup>−1</sup> s<sup>−1</sup>)</th></tr><tr><th colspan="1" rowspan="1"/><th align="left" colspan="1" rowspan="1">Solution</th><th align="left" colspan="1" rowspan="1">Surface</th></tr></thead><tbody><tr><td align="left" colspan="1" rowspan="1">P<sub>0</sub>T<sub>0</sub></td><td align="left" colspan="1" rowspan="1">12.0 ± 0.6</td><td align="left" colspan="1" rowspan="1">0.57 ± 0.04</td></tr><tr><td align="left" colspan="1" rowspan="1">P<sub>3</sub>T<sub>3</sub></td><td align="left" colspan="1" rowspan="1">7.2 ± 0.3</td><td align="left" colspan="1" rowspan="1">0.24 ± 0.01</td></tr><tr><td align="left" colspan="1" rowspan="1">P<sub>4</sub>T<sub>3</sub></td><td align="left" colspan="1" rowspan="1">3.0 ± 0.1</td><td align="left" colspan="1" rowspan="1">0.083 ± 0.003</td></tr><tr><td align="left" colspan="1" rowspan="1">P<sub>4</sub>T<sub>4</sub></td><td align="left" colspan="1" rowspan="1">2.0 ± 0.1 (fast)</td><td align="left" colspan="1" rowspan="1">0.032 ± 0.001</td></tr><tr><td colspan="1" rowspan="1"/><td align="left" colspan="1" rowspan="1">0.48 ± 0.01 (slow)</td><td colspan="1" rowspan="1"/></tr></tbody></table><table-wrap-foot><fn><p>Errors represent uncertainty in fitting single trial data to either <xref ref-type="disp-formula" rid="e2">Equation 2</xref> (solution) or <xref ref-type="disp-formula" rid="e4">Equation 4</xref> (surface); trial-to-trial errors are, at most, 7%.</p></fn></table-wrap-foot></table-wrap></sec></back></article>