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Nucleic Acids Res. 2006; 34(3): e26.
Published online Feb 13, 2006. doi:  10.1093/nar/gnj024
PMCID: PMC1369288

On-chip non-equilibrium dissociation curves and dissociation rate constants as methods to assess specificity of oligonucleotide probes

Abstract

Nucleic acid hybridization serves as backbone for many high-throughput systems for detection, expression analysis, comparative genomics and re-sequencing. Specificity of hybridization between probes and intended targets is always critical. Approaches to ensure and evaluate specificity include use of mismatch probes, obtaining dissociation curves rather than single temperature hybridizations, and comparative hybridizations. In this study, we quantify effects of mismatch type and position on intensity of hybridization signals and provide a new approach based on dissociation rate constants to evaluate specificity of hybridized signals in complex target mixtures. Using an extensive set of 18mer oligonucleotide probes on an in situ synthesized biochip platform, we demonstrate that mismatches in the center of the probe are more discriminating than mismatches toward the extremities of the probe and mismatches toward the attached end are less discriminating than those toward the loose end. The observed destabilizing effect of a mismatch type agreed in general with predictions using the nearest neighbor model. Use of a new parameter, specific dissociation temperature (Td-w, temperature of maximum specific dissociation rate constant), obtained from probe–target duplex dissociation profiles considerably improved the evaluation of specificity. These results have broad implications for hybridization data obtained from complex mixtures of nucleic acids.

INTRODUCTION

Microarrays represent the apex of nucleic acids hybridization-based methods in terms of throughput and number of applications. In addition to their widespread use in gene expression studies (1,2), they are also important in comparative genomics (35), microbial gene detection (613), single nucleotide polymorphism analysis and re-sequencing (1417). Specificity of hybridization signal is critical in all cases. It is especially important in applications involving hybridization of samples with complex uncharacterized background [e.g. microbial detection (1821)]. Specificity at the probe design level is provided by selecting oligonucleotide probes that are perfect matches (i.e. identical in complementary sequence) to their intended targets, differ significantly compared with all other sequences, and have a narrow range of melting temperature (Tm). Although it is well known that attachment of probes to surfaces can dramatically influence the hybridization behavior of duplexes (14,2225), most probe design for microarrays employs rules established with data collected from hybridization carried out in solution (26,27).

At the experimental level, specificity is provided by hybridization conditions that minimize hybridization of mismatch targets to the probes (10,28) or by conducting hybridization over a range of temperature (2935). Another common approach is to design a set of mismatch (MM) probes that may be compared in their signal intensity with the perfect match (PM) probes. Data analysis techniques then evaluate the specificity provided by the above approaches. Comparison of dissociation temperature [Td-50, the temperature at which 50% of the initial probe-target duplex is washed off, (30,31)] or signal intensity for PM probe compared with MM probe are the common examples at this level. Since probe-target duplexes containing one or more mismatches are less stable than perfect match probe-target duplexes, these MM duplexes can be identified because of their lower dissociation temperature, Td-50 (the temperature at which 50% of the initial signals are washed out) compared with the PM duplex (2934).

The purpose of this study was to: (i) assess the difference in hybridization behavior of PM and MM probes in terms of their predicted Tm and experimentally determined Td-50, and (ii) determine if alternative parameters obtained from the non-equilibrium dissociation curves (namely, the dissociation rate constant—kd and the maximum specific dissociation temperature—Td-w) are more discriminatory than dissociation temperature, Td-50. To this end, we used in situ synthesized microfluidic chips containing an extensive set of 18mer probes to obtain Td-50 and Td-w for a number of gene targets. We compared experimental variation in signal intensities and Td-w between a variety of perfect match and mismatch probes with predictions of the nearest neighbor model.

MATERIALS AND METHODS

Oligonucleotide arrays

Sequences of 11 genes from Escherichia coli strain O157:H7 RIMD 0509952 (36) (aroE, clpX, cstA, glyA, lysP, rpoS, mdh, stx1, stx2, eae and uidA) and one gene from Shigella flexneri 2A 2457T (virA) were used to design 935 PM 18mer oligonucleotide probes. For 352 PM probes targeting aroE, clpX, cstA, glyA, lysP, rpoS, mdh and virA genes, three single mismatch 18mer probes created randomly with respect to both position and type of mismatch were also designed resulting in a total of 1056 MM probes. For 578 PM probes, additional 18mer MM probes with a single mismatch in the center (position 9) were designed. Furthermore, 20, 25, 35 and 45mer probes for the aroE gene and 20mer probes for the stx1, stx2, eae and uidA genes were added. These probes were synthesized in situ on microfluidic chips by Xeotron (Houston, TX, now part of Invitrogen, Carlsbad, CA) (37). Briefly, the glass-silicon chip surface was first derivatized with an N-(3-triethoxysilylpropyl)-4hydroxybutyramide linker (Gelest, Morrisville, PA) and then a spacer consisting of Ts and C18 spacers for an effective length of 12 bp was directly synthesized on the linker's hydroxyl group using the phosphoramidite chemistry. The oligonucleotides were synthesized on top of this spacer with an estimated density of 1 molecule per 200 square angstroms.

DNA and target preparation

Fragments of ~600 bp including the sequences targeted by the oligos on the chip were amplified from DNA of E.coli strain O157:H7 RIMD 0509952 (36) (aroE, clpX, cstA, glyA, lysP, rpoS, mdh, stx1, stx2, eae and uidA) and from DNA of S.flexneri 2A 2457T (virA). A purified PCR product mixture (6.8 × 10−14 mol of each amplicon) was aminoallyl-dUTP labeled (Sigma, St Louis, MO) with the Klenow-based Invitrogen DNA labeling system (Invitrogen, Carlsbad, CA) as described previously (38). For replicate measurements on the same chip, aliquots from the same pool of labeled DNA were used. For different chips, aliquots from different pools were used. Genomic DNA was prepared as described previously (38). The Cy3 dye was used as the fluorescent label in all experiments.

Microarray hybridization

The in situ synthesized chips were prehybridized, hybridized and washed in a M-2 microfluidic station (Xeotron Corporation, Houston, TX, now part of Invitrogen, Carlsbad, CA) at a flow rate of 500 µl/min. Hybridization buffer was 6× SSPE, 35% formamide, 0.4% Triton X-100 for hybridizations of only PCR products and 6× SSPE, 25% formamide, 0.4% Triton X-100 for hybridizations of samples containing genomic DNA. Chips were prehybridized with 6× SSPE, 0.2% Triton X-100 and then with hybridization buffer for 2 min each. All SSPE buffers were made from a stock of 18× SSPE, which is 2.7 M NaCl, 180 mM Na2PO4, 18 mM Na2EDTA (pH adjusted to 6.6 with HCl). Labeled target was suspended in 50 µl hybridization buffer, denatured at 95°C for 3 min, cooled on ice for 1 min, filtered through a 0.22 µm Costar spin filter and then hybridized to the chip for 14–15 h at 20°C. Since the residual prehybridization buffer in the Xeotron chip is ~50 µl, the final hybridization volume was ~100 µl. After hybridization the chip was washed at 20°C with hybridization buffer, with 6× SSPE, 0.2% Triton X-100, with 1× SSPE, 0.2% Triton X-100 and finally with 6× SSPE for 2.2 min each. The chip was scanned with a GenePix 4000B laser scanner (Axon Instruments, Union City, CA). All solutions were filtered through a 0.22 µm filter to prevent clogging of the microfluidic channels. The high stringency wash buffer was degassed under vacuum.

Melting curve profiles

To create a dissociation profile, a hybridized chip was washed at 25°C with high stringency wash buffer (20 mM NaCl, 10 mM Na2PO4, 5 mM Na2EDTA, pH adjusted to 6.6 with HCl) for 1.4 min and then scanned. Cycles of washing and scanning were repeated manually at 1°C intervals until 60°C was reached. At the end of this series, the chip was stripped further by washing with distilled water (three times each for 2.2 min at 60°C).

Data acquisition

Hybridization signal intensities were extracted with GenePix 5.0 software (Axon Instruments, Union City, CA), yielding values between 0 and 65 535 arbitrary units (a.u.). For each dissociation temperature, a background value was determined as the median of the 95% empty spots with the lowest signals on the array and subtracted from each signal at the corresponding temperature. Background values were between 50 and 80 a.u. If a spot signal after background subtraction was less than three times the standard deviation of the background, it was set to 3 SD of the background.

Data flagging

Bad curves were excluded from analysis by flagging them when one or more of the following conditions were satisfied: (i) the initial signal was <200 a.u. or saturated; (ii) the R2 of the linear fit to calculate Td-50 was below 0.9; (iii) the Td-50 value was outside the points used for the linear fit; (iv) the signal at Td-50 or at Td-w was <5 times the standard deviation of the background signal intensity; (v) the interpolated Td-w was more than 1°C different from the actually used wash temperature yielding maximum kd; (vi) the coefficient of variation for the mean Td-50 or Td-w from the five replicate experiments exceeded 5%.

Five replicate hybridizations (two on one chip and three on a second chip) of PCR product mixtures were used to calculate the mean of Td-50, Td-w and log2(PM/MM) ratios for each probe. Probes flagged in any of the five replicates were excluded from Td-50 and Td-w analysis. For the log2 (PM/MM) ratios, all those PM–MM pairs were analyzed that had an initial PM signal intensity higher than 128 times three standard deviations of the background (between 700 and 2600 a.u. depending on chip). Following this protocol, log2 ratios up to nearly seven, which is about the 95th percentile observed for the probe set, can be determined relatively accurately for all probes. Multiple pairwise comparisons were made with JMP4 (SAS Institute).

Nearest neighbor calculations

Melting temperatures (Tm), free energy changes (ΔG0), enthalpy changes (ΔH0) and entropy changes (ΔS0) were calculated with the nearest neighbor model using published parameters for PM and MM duplexes assuming a two-state model (26,27). Contributions of the dangling end in computing the above parameters were neglected. For calculating Tm, a probe concentration of 10 nM was assumed. For calculation of ΔG0 in the hybridization buffer, 43°C instead of the actual 20°C degrees was used since the buffer contained 35% formamide, which is expected to destabilize duplexes in a way equivalent to increasing the temperature by 21–25°C (33,39).

Data analysis

Dissociation curve parameters were computed using Excel (Microsoft, Redmond, WA). Median of signal intensities at 26, 27 and 28°C was used as the initial signal and median of signal intensities at temperatures from 56 to 60°C was used as the final signal for a dissociation curve. The difference between the initial and final signal was defined as ‘range’. Dissociation curves were normalized by setting the initial value to 1, the end point to 0 and scaling all other values linearly. For hybridizations with PCR products, dissociation curves were linear in the central range of the hybridization temperature. Therefore, the best linear fit through nine points of each dissociation curve was used to calculate Td-50 as the temperature where 50% of the range was washed off, i.e. where the normalized signal intensity equals 0.5. For hybridizations with genomic DNA, a linear fit through three points closest to the 50% value of the initial signal was used to interpolate Td-50.

The hybridization of a target to a probe can be described with the following equation:

[Probe]+[Target]kakd[ProbeTarget].
1

The above equation assumes there are no effects of probe–probe interactions, target–target interactions, or secondary structures of probes and targets. For a non-equilibrium dissociation curve where the target is washed away instantaneously, the association constant, ka, becomes zero and the decrease in hybridization signal intensity (I) with time (dt) at a given temperature can be described by the following first order equation:

dI=Ikddt.
2

In the integrated form, Equation 2 can be written as:

It=I0ekd(tt0)
3

where It is the intensity after the wash, I0 is the intensity before the wash, kd is the temperature-dependent dissociation rate constant and (tt0) the washing time. Hence, the dissociation rate constant for each probe–target duplex at each temperature can be obtained by calculating kd at the corresponding temperature using the following equation:

kd=lnI0lnIttt0
4

The temperature dependence of kd is expected to follow the Arrhenius equation:

kd=AeEaRT
5

where, A is the Arrhenius constant, Ea the activation energy and R the gas constant.

For calculation of Td-w (temperature at the maximum measured dissociation rate constant) the signals were transformed by taking their natural logarithm. Slopes at the resulting ‘ln(I) versus T’ curve yielded the dissociation rate constant (k). To smooth the ‘k versus T’ curve, k at a given temperature was calculated by taking the linear slope over either five degrees (including two temperature points before and after the given temperature) or nine degrees (including four temperature points before and after the given temperature). For hybridization with PCR products, nine points were used. For hybridization involving genomic DNA, five points were used in order to increase resolution. The temperature at the maximum dissociation rate constant (Td-w) was obtained by interpolating the temperature at which the first derivative (approximated by the slope through three consecutive points) of the ‘k versus T’ curve was zero.

RESULTS

Td-50 and Td-w for dissociation curves of PCR products

Of the 1991 non-equilibrium dissociation curves obtained from 935 PM probes (18mer) and 1056 randomly created single MM probes, 597 (30%) were flagged as bad quality in one or more of the five replicate hybridizations of PCR products. The single most important criterion for flagging curves was the initial signal intensity. Of the flagged curves, 76% had an initial intensity below 200 a.u. and 85% were below 500 a.u. Most flagged curves (81%) were from MM probes. Examples for normalized dissociation curves and dissociation rate constants (kd) for a PM probe and two single-base-pair MM probes are shown in Figure 1. According to the Arrhenius equation, kd should continually increase with temperature (dashed lines in Figure 1B), but practically it has a maximum. The temperature at which the measured kd reaches this maximum is a critical point on the dissociation rate curve and is referred as Td-w. It represents the temperature where the target has essentially been washed off, i.e. the abundance of targets bound to the probe is insufficient to yield a sensible measurement of the real kd and the Arrhenius equation no longer holds true.

Figure 1
Dissociation profiles from a perfect match (filled triangles) probe and two probes containing a single base pair mismatch (empty and filled circles). (A) Normalized signal intensities. Probe sequences are given with the mismatches in bold italics. Td-50 ...

Correlation of Td-50 and Td-w with nearest neighbor melting temperature (Tm)

Td values of PM probes obtained by the traditional dissociation curve method (Td-50) and the new maximum rate of dissociation method (Td-w) were compared with Tm values calculated with the nearest neighbor model. The correlation between Td-w and Tm was better compared with the correlation between Td-50 and Tm (Figure 2). Also Td-w computed for 18 and 20mer probes with initially saturated signal intensities corresponded well with Td-w values for non-saturated probes with similar Tm (open triangles in Figure 2).

Figure 2
Correlation between Tm and Td-w (A), and Tm and Td-50 (B) for PM probes. Black circles: 18mer, not saturated (n = 819); open triangles: 18 and 20mer saturated (n = 25). Values are means of five experiments. The R2 value for the linear fit between Tm and ...

Effect of mismatch position

For the 352 PM probes that had each three randomly created single mismatch probes, the effect of mismatch position on initial signal intensity and Td-w was evaluated. Log2(PM/MM) of the initial signal intensity and ΔTd-w (i.e. Td-w for PM − Td-w for MM) were calculated and plotted against the position of the mismatch (Figure 3). Both curves have an inverse U-shape, which indicates that the best discrimination between PM and MM is better for mismatches near the center of the probe than for mismatches near the terminal positions. For example, the signal intensity of a probe with a mismatch at position 9 was on average only ~4% of the corresponding PM probe signal intensity. Td-w for the MM was more than 4°C lower. In contrast, mismatches at the very end of the 18mer had signal intensities that were ~50% the corresponding PM probe signal intensity with Td-w values only about 1°C lower. The effect of the mismatch position on ΔTd-50 was similar to that observed for ΔTd-w (data not shown).

Figure 3
Influence of the position of a single base pair mismatch on the initial signal intensity (A) and on ΔTd-w (B). Boxes indicate the range from the 25th to 75th percentile, whiskers the 10th and the 90th percentile. The median is given as a solid, ...

Effect of mismatch type

For some mismatch positions no significant effect of position on log2(PM/MM) or on ΔTd-w was observed (Tukey-Kramer, α = 0.05). Probes with mismatches in these positions [positions 5–11 for log2(PM/MM) and 4–14 for ΔTd-w] were grouped by mismatch type and the average log2(PM/MM) and ΔTd-w were calculated for the group. To designate mismatch type, we used the first letter to denote the base in the probe and the second letter to denote the base in the target (Figure 4). Because the targets are the same for PM and MM probes, a C-T mismatch, for example, means that the corresponding PM probe has an A instead of a C at that position resulting in an A-T Watson–Crick pair for the PM probe–target duplex. For a T-C mismatch, the perfect match in the corresponding PM probe–target duplex would be a G-C base pair. Because the effects of mismatches are measured as differences in parameters obtained from MM probes and their corresponding PM probes, a T-C mismatch (compared to a G-C perfect match) is generally more discriminating than a C-T mismatch (compared with a A-T perfect match) because G-C is a stronger bonding base-pair than A-T. Log2(PM/MM) values were compared with differences in ΔG0 of the PM-target and MM-target duplexes (Figure 5A) because, on average, the log(signal) of all 18mer PM probes on the chip linearly correlated with ΔG0 of probe target duplexes (data not shown). Values for ΔTd-w were compared with values for ΔTm (defined as the difference in Tm between PM and MM) (Figure 5B). Overall, there was a good correlation between measured values and values calculated with the nearest neighbor model. However, for both the log2 ratios as well as the ΔTd-w values some of the values are probably an underestimation. For MM probes with initial intensities less than five times the standard deviation of the background, the actual log2(PM/MM) ratio is likely to be larger than the measured one. For computing ΔTd-w, MM probes with low intensities were excluded. Most of these excluded probes would probably have a ΔTd-w lower than average. Indeed, mismatch types with higher predicted discrimination were also more likely to have a very low MM signal or to be excluded from Td-w analysis (Table 1).

Figure 4
Designation of MM-types. In naming MM-types, the first letter denotes the base in the probe (solid line), the second the one in the target (dashed line). An example for a T-C (middle) and a C-T (right) mismatch with the corresponding PM probe (left) are ...
Figure 5
Correlation between predicted and measured effects of mismatch type on initial signal intensity (A), and on ΔTd-w (B). Group means with 95% confidence intervals are given. R2 values are for the best linear fit between calculated and measured group ...
Table 1
Sample sizes for data plotted in Figure 5

Nearly all MM probes had significantly lower Td-50 (92%) and Td-w (94%) than their corresponding PM probes (α = 0.05, two-tailed t-test, five replicate experiments). Also the majority of terminal and penultimate (second to last) mismatches were detected by their dissociation profiles (79% based on Td-50 and 88% based on Td-w) (Table 2). Toward the surface distal 5′ end (position 1) the resolution of near terminal mismatches was better than toward the surface proximal 3′ end (position 18) (Table 2). Based on Td-w, 100% of mismatches at position 2 and 98% of mismatches at position 1 were resolved, whereas only 84% of mismatches between position 14 and 18 (i.e. near the 3′ end) were resolved. Interestingly, most of the unresolved mismatch types were G-T, C-A and C-T mismatches (24 out of 31). These three mismatch types were significantly more likely to be unresolved than the other nine mismatch types [residual analysis of the contingency table, α = 0.05 (40)].

Table 2
Significant differences in Td-50, Td-w and initial signal intensities between perfect match and mismatch probes

Analysis of dissociation curves influenced by cross-hybridization

The data above were obtained from low complexity samples (i.e. twelve 600 bp PCR fragments resulting in a total of ~7 kb); therefore, we observed minimal cross-hybridization, as evident in the overall strong correlation between Tm and Td-50 (Figure 2). When hybridizing more complex samples, e.g. whole genomes containing about 5000 genes (~5 Mb), more substantial cross-hybridization is expected and probes without a perfect match target in the sample can still give high signals, especially at low temperatures. To test the influence of cross-hybridization on dissociation curve behavior, genomic DNA from E.coli Sakai spiked with different amounts of PCR products were used for hybridization. Dissociation curves of PM duplexes are normally of a sigmoid shape, but they change to a more linear shape and then to an exponential decay shape with increasing amounts of cross-hybridization (Figure 6). A target melting with a lower Td-50 than expected from a PM target indicates hybridization of mismatched targets. These can be defined targets containing a single nucleotide mismatch (Figure 1A) or less well defined non-specific cross-hybridization signals resulting from a complex background (Figure 6A, C and E). With complex background DNA, it is difficult to determine whether 100% of the signal is due to cross-hybridization, or whether it is a combination of signals due to cross-hybridization and perfect match target. In the case of a combined signal originating from a mixture of non-specific and specific targets, a decision based on the Td-50 alone would lead to a false negative call. Td-50 only can detect cross-hybridization, but does not indicate if the signal is from unspecific background, a single mismatch target or a combination of unspecific and specific targets. Td-w, on the other hand, should be able to detect such differences. Unspecific signals wash off earlier and show a higher kd than the specific signal in the beginning of the melting curve. After the unspecific signal is washed off, the kd and Td-w of the specific signal will still reveal the presence of the specific target. Indeed, most of the Td-w values obtained from the spiked samples showing cross-hybridization were close to Td-w values obtained from PM targets alone, whereas Td-50 values were generally much lower (Figure 7). For a few probes with extensive cross-hybridization even the Td-w may substantially decrease, making it difficult to distinguish the cross-hybridization signal from the specific hybridization signal (Figure 6F). For this probe, with increasing amount of genomic DNA in the sample, the Td-w shifts more toward lower temperatures, indicating an increasing amount of cross-hybridization (Figure 6F). In contrast, Td-50 has nearly the same low value in all samples containing genomic DNA and cannot detect the different amounts of cross-hybridization (Figure 6E). Generally, the 18mer probes proved too short and unspecific when only unspiked genomic DNA was hybridized.

Figure 6
Normalized dissociation curves (top panels A, C, E) and dissociation rate constants kd (bottom panels B, D, F) of three PM probes showing various degrees of cross-hybridization. Hybridization was carried out with 4.2 µg of PCR-products only (filled ...
Figure 7
Impact of cross-hybridization on computed Td-w (A and B) or Td-50 (C and D). For cross-hybridization, 3.4 µg genomic DNA was spiked with 400 ng PCR products (A and C) or 3.7 µg genomic DNA was spiked with 45 ng PCR products (B and D). ...

Another approach to assess the amount of cross-hybridization is by comparing the PM signal with the signal from a MM probe with a single mismatch at the center of the probe. For 578 such PM–MM probe pairs, signals of PM and MM were compared. In the absence of cross-hybridization, signals from MM probes are consistently lower than signals from PM probes. In three of the five replicates using PCR products, none of these MM probes had a signal higher than the PM probes. In one of the five replicates four, in another one five MM probes, had a slightly higher signal, but four of those were low intensity spots (less than twice the background level) on both chips. The situation changes when hybridizing more complex samples. For example, the number of MM probes with a signal higher than the PM probes increased from 19 to 37 to 111 when the ratio of PCR product spiked in genomic DNA (expressed as ng of PCR product to ng of genomic DNA) changed from 400:3400 to 45:3700 to 0:3800, respectively. This shows that cross-hybridization can be very different for PM and MM probes and use of MM probes to estimate cross-hybridization of PM probes may be problematic in complex samples. But the Td-w for all the MM probes in the spiked samples was lower than for the PM probes and Td-w values for most PM probes were in the range expected from values obtained without cross-hybridization (Figure 7).

DISCUSSION

This study shows that monitoring the dissociation rate constant of non-equilibrium melting curves considerably improves the interpretation of hybridization signals. Specifically, we demonstrate here that the temperature where the measured dissociation rate constant is maximal, Td-w, obtained from non-equilibrium dissociation curves has several advantages over the conventional measure, Td-50. Compared with Td-50, Td-w had better correlation with Tm over a wide range of temperature (Figure 2). Computation of Td-w does not depend on initial signal intensity and is thus more reliable even for probes having saturated signals at lower temperatures (Figure 2) or probes with cross-hybridization (Figures 6 and and7).7). Moreover, the method uses the dissociation rate constant, which is the actual physical parameter measured during a non-equilibrium washing curve. Besides the Td-w used here, other methods of analyses based on the dissociation rate constant might be useful, such as absolute values of kd at given temperatures, temperatures where kd has a certain value or the run of the kd-curve. For example, the kd of a single mismatch target starts off at a low level, similar to the kd from the corresponding perfect match target, but then increases more rapidly with increasing temperatures (Figure 1B). In contrast, the signals from a combination of mismatch and perfect matched targets yielded larger kd at lower temperatures, but gradually approached the kd values of the perfect match targets when more and more of the mismatched targets are lost and the fraction of perfect match target contributing to the signal increases (Figure 6B and D). This shows that the dissociation rate constant is a promising parameter in interpreting signals from more complex samples leading to binding of several different targets to one probe. The resolution of such mixed signals gets better the more accurately kd is determined at each single temperature point. In order to reduce noise, the data were smoothed in this study by calculating the slopes at the ‘ln(I) versus T’ curve over several temperature points in a linear fit, which of course lowers the resolution. Advanced technical setups (cycles between washing and scanning were carried out manually in this study), producing data with less noise and also improved smoothing methods, should be able to further increase the resolution and the specificity of this method. For some of the mixed probe–target duplexes, a decomposition of the observed curve and a quantification of the contributions of each target to the overall signal should also be achievable.

Td-w values from PM duplexes correlated well with Tm obtained from the nearest neighbor model, suggesting that parameters obtained from PM duplexes in solution can be applied to duplexes on the array. This is possible despite the fact that Tm values are based on thermodynamic equilibrium and Td values are based on non-equilibrium dissociation measurements. Thus, the dissociation rate constant is the principal sequence-dependent factor in determining probe–target binding thermodynamics, and the association constant (Equation 1) is rather sequence independent. For equilibrium values on Affymetrix chips containing 25mer, Held et al. (41) observed an overall good correlation between measured intensities and free energies calculated with parameters obtained from solutions; however, in contrast, Zhang et al. (42) found only a weak correlation between nearest neighbor values fitted to Affymetrix chip data and values obtained from solution.

Effect of mismatch type

For duplexes containing single-base pair mismatches, there was on average a good correlation between predicted and measured values of differences in signal intensities after overnight hybridization and also between differences in dissociation temperatures of MM and PM duplexes. As predicted by the two-state nearest neighbor model, G-T and G-A mismatches were least discriminating and C-C, T-C and A-C mismatches were most discriminating (Figure 5). The same effects of mismatch types were predicted by simulations using the software Oligonucleotide Modeling Platform (OMP, DNA Software, Inc., Ann Arbor, MI) by Lee and co-workers (43). OMP uses a multi-state model instead of the two-state model and should generally produce more accurate predictions. We observed a considerable variability among different probes with the same mismatch type. The use of formamide buffer and the presence of secondary structures or probe–probe interactions may account for the differences in expected and observed log ratios after overnight hybridizations. To calculate thermodynamic parameters in formamide buffer, we assumed that 1% increase in formamide concentration has a destabilizing effect equivalent to an increase in temperature of 0.6–0.7°C (33,39). However, formamide may destabilize some base pairs differently than others (39). Introduction of a mismatch not only affects the probe–target duplex, but may also change the stability of the probe's secondary structures and of probe dimers, thus impacting the availability of MM-probes for target binding, compared with PM probes.

One reason for differences between predicted and measured ΔTd-w values is that curves yielding useful parameters are biased, because for several probes the mismatch was so destabilizing that signals were too low to be analyzed accurately. The percentage of excluded probes was generally higher for mismatch types with higher predicted destabilizing effects (Table 1), further supporting the correlation between nearest neighbor predictions and measured values.

Moreover, some base-pairings might behave very differently depending on next to nearest neighbors or sequence position. For example, some C-T, C-A and G-T mismatches near the 3′ end had the same or even a higher Td-w than their PM probes, although C-T and C-A are expected to be more destabilizing than several other mismatch types (Figure 5 and Table 1).

Because the nearest neighbor predictions are based on equilibrium values, the variation observed among MM probes might also be based on a larger influence of mismatches on the association constant, compared with PM probes. Ideally, nearest neighbor parameters should be established for non-equilibrium melting curves, so that the melting can be predicted from the probe sequence.

Effect of mismatch position

A major difference between predictions based on solution parameters using the two-state nearest neighbor model and our chip data was that the mismatch position had an effect on differences in initial signal intensities [log2(PM/MM)] as well as on both ΔTd-w and ΔTd-50. Mismatches in the central part of the probe were more destabilizing than mismatches near the extremities, leading to an inverse U-shaped relationship between mismatch position and destabilizing effect of the mismatch. For 25mer PM duplexes on Affymetrix chips, modeling suggested that Watson–Crick base pairs in the center of a probe contributed more to the stability of the duplex than base pairs toward the ends (42,44). Our study shows an analogous effect for mismatches, which have a greater destabilizing effect when placed around the middle part of a probe than toward the ends of the probe. For hybridizations in solution, the same U-shaped position effect has been found for duplexes containing a single 3-nitropyrrole artificial mismatch at all possible positions in a 15mer (45). Although the OMP software correctly predicts smaller destabilizing effects of mismatches at the three end positions, it does not predict a position effect for positions 4 and higher (43) and might therefore underestimate the importance of mismatch position.

Effect of attachment surface on destabilization

As indicated earlier, the 3′ end of the oligonucleotide probes was attached to the surface of the chip. The data suggest an asymmetry that mismatches near the surface distal 5′ end are more destabilizing than the ones near the surface proximal 3′ end. A similar observation has been reported for 60mer oligonucleotide arrays (22), where maximum discrimination was observed for mismatches ~10 bases away from the distal end, whereas single base pair mismatches within the first 30 bases near the proximal end did not show a considerable destabilizing effect. One hypothesis for this effect is that the duplex and the free dangling ends (i.e. single-stranded target not bound to a probe sequence) nearer to the surface get partly immobilized in the DNA film. In contrast, the more freely moving ends protruding into the solution may dissociate and diffuse away more easily when destabilized by a mismatch.

In conclusion, we have established experimentally that the physical parameter measured during a non-equilibrium melting curve, i.e. the dissociation rate constant, kd, is very useful for the interpretation of hybridization signals. This analysis method is especially valuable when hybridization of complex samples leads to simultaneous binding of specific and unspecific targets to the same probe.

Acknowledgments

This project was funded in part by the MSU foundation, the Michigan Economic Development Corporation (GR-476 PO 085P3000517) and the NIH (1 R01 RR018625-01). Funding to pay the Open Access publication charges for this article was provided by the MSU Foundation, Michigan Economic Development Corporation, and the NIH.

Conflict of interest statement. None declared.

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