Nicholas
Spurlock
a,
William E.
Gabella
b,
Dalton J.
Nelson
a,
David T.
Evans
a,
Megan E.
Pask
a,
Jonathan E.
Schmitz
c and
Frederick R.
Haselton
*a
aDepartment of Biomedical Engineering, Vanderbilt University, PMB 351631, Nashville, TN, USA. E-mail: rick.haselton@vanderbilt.edu
bDepartment of Physics and Astronomy, Vanderbilt University, Nashville, TN, USA
cDepartment of Pathology, Microbiology and Immunology, Vanderbilt University Medical Center, Nashville, TN, USA
First published on 25th March 2024
In previous reports, we described a PCR cycle control approach in which the hybridization state of optically labeled L-DNA enantiomers of the D-DNA primers and targets determined when the thermal cycle was switched from cooling to heating and heating to cooling. A consequence of this approach is that it also “adapts” the cycling conditions to compensate for factors that affect the hybridization kinetics of primers and targets. It assumes, however, that the hybridization state of the labeled L-DNA analogs accurately reflects the hybridization state of the D-DNA primers and targets. In this report, the Van't Hoff equation is applied to determine the L-DNA concentration and ratio of L-DNA strands required by this assumption. Simultaneous fluorescence and temperature measurements were taken during L-DNA controlled cycling, and the optical and thermal switch points compared as a function of both total L-DNA concentration and ratio of strands. Based on the Van't Hoff relationship and these experimental results, L-DNA best mirrors the hybridization of PCR primers and targets when total L-DNA concentration is set equal to the initial concentration of the D-DNA primer of interest. In terms of strand ratios, L-DNA hybridization behavior most closely matches the behavior of their D-DNA counterparts throughout the reaction when one of the L-DNA strands is far in excess of the other. The L-DNA control algorithm was then applied to the practical case of the SARS-CoV-2 N2 reaction, which has been shown to fail or have a delayed Cq when PCR was performed without nucleic acid extraction. PCR Cq values for simulated “unextracted” PCR samples in a nasopharyngeal background and in an NaCl concentration similar to that of viral transport media were determined using either the L-DNA control algorithm (N = 6) or preset cycling conditions (N = 3) and compared to water background controls run in parallel. For preset cycling conditions, the presence of nasopharyngeal background or a high salt background concentration significantly increased Cq, but the L-DNA control algorithm had no significant delay. This suggests that a carefully designed L-DNA-based control algorithm “adapts” the cycling conditions to compensate for hybridization errors of the PCR D-DNA reactants that produce false negatives.
Other than creating L-DNA strands with exact sequence homology to their D-DNA counterparts, no clear guiding theory and practice has been proposed to ensure that the L-DNA analogs closely mimic the D-DNA molecular events during the annealing and melting phases of a PCR reaction. In standard PCR reactions, primers complementary to the expected target are added in extremely high concentrations relative to the target concentration (i.e., on the scale of 6–12 orders of magnitude greater, depending on initial target concentration). Primers anneal to any target strands present, and during the extension phase these primers are incorporated into new copies of the amplicon sequence. Until the plateau phase is reached, this results in an increase in the number of amplicons and a decrease in the number of primers with each PCR cycle. Several explanations exist for the plateau phase, including exhaustion of PCR reagents (primers, dNTPs, and polymerase),10,11 and inhibition of polymerase activity by an abundance of double-stranded amplicon.12,13 Regardless of the explanation for the plateau phase, the ratio of the D-DNA components changes exponentially in the pre-plateau cycles of the reaction. An obvious concern, therefore, is how accurately the fixed concentration of the L-DNA analogs represents the changing PCR primer and amplicon concentrations.
For both D-DNA and L-DNA, the theoretical relationship between the fraction of DNA in a hybridized state (f) at a given temperature Tf and total concentration of complementary strands ([C]) is described by Van't Hoff kinetic theory14
![]() | (1) |
![]() | (2) |
![]() | (3) |
In this expression, if C1 is set to be equal to C2, eqn (3) simplifies to eqn (1). If f is set to 0.5, eqn (3) simplifies to eqn (2).
The Van't Hoff equation suggests that both total concentration and strand ratios affect the annealing behavior of both L-DNA and D-DNA. For the L-DNA analogs, C1 and C2 remain constant over all cycles of a PCR reaction, while for D-DNA strands the concentrations and primer-target strand ratio change with each PCR cycle. Since these changing concentrations affect the value of Tf, eqn (3) surprisingly suggests that despite the preset times and temperatures traditionally used in PCR, the temperature for a fixed fraction of primers to anneal is not constant.
In addition to eliminating the need to preset the reaction temperature, this L-DNA control approach also promises to “adapt” cycling conditions to compensate for variation in reaction conditions.1 For example, performing PCR directly using a sample without nucleic extraction has proven useful in screening applications, particularly in resource limited conditions such as point of care settings.16 But because sample preparation is not incorporated into these direct PCR workflows, false negatives can occur. One particular cause of these false negatives is that unextracted reaction interferents, e.g. salts and proteins, may be present and affect strand interactions in PCR. An example of this is the CDC 2019-Novel Coronavirus (2019-nCoV) Real-Time RT-PCR Diagnostic Panel, which has been shown to produce false negatives when performed with unextracted nasopharyngeal samples without annealing temperature adjustment.17 In this case, a small variation in annealing temperature (on the scale of 2 °C) resulted in a Cq delay of 5 or greater.18 As these variations in primer-target hybridization behavior should also be reflected in changes in the hybridization behavior of their L-DNA analogs, the L-DNA control algorithm can account for them—provided other factors, such as total concentration and strand ratio, are accounted for.
In this report, experimental data guided by the Van't Hoff equation are used to predict the D-DNA hybridization kinetics in a PCR reaction. The L-DNA total concentration and the L-DNA strand ratio are then determined experimentally so that their hybridization state at a particular temperature matches the D-DNA reactants as closely as possible. These theoretical optimizations are combined with practical considerations, such as minimum detectable fluorescence signal and reagent cost, to show that L-DNA additives provide an accurate mirror for D-DNA reactants across almost all cycles, but especially the early cycles where C1 (primers) is far in excess of C2 (amplicons). These optimizations are then applied to SARS-CoV-2, demonstrating the “adaptive” nature of the L-DNA cycle control approach and reducing the false negatives in unextracted nasopharyngeal testing.
Description/name | Sequence (5′-3′) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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a HEX = hexachloro-fluorescein, FAM = fluorescein, TEX = texas red, Cy5 = cyanine 5, BHQ 1 and BHQ 2 = black hole quenchers 1 and 2. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Control L-DNA | Anneal sensor fluorescent strand | TEX—TTACAAACATTGGCCGCAAA | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Anneal sensor quencher strand | TTTGCGGCCAATGTTTGTAATCAGT—BHQ2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Melt sensor fluorescent strand | HEX—ACAAGAAAGGGATCTTCACTCGCGACCGCAAACCGA AGTCGGCGGCTTTTCTGCTGCAAAAACGCTGGACTGGCATG | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Melt sensor quencher strand | CATGCCAGTCCAGCGTTTTTGCAGCAGAAAAGCCGCCGACTTCGGTTTGCGGTCGCGAGTGAAGATCCCTTTCTTGT—BHQ2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
RT beacon2 | FAM—GCGAGAAAAAAAAAAAAAAACTCGC—BHQ1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Labeled D-DNA | N2 fluorescent forward primer | HEX—TTACAAACATTGGCCGCAAA | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N2 quencher reverse complement | TTTGCGGCCAATGTTTGTAATCAGT—BHQ2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
SARS CoV2 PCR assay | N1 forward primer | GACCCCAAAATCAGCGAAAT | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N1 reverse primer | TCTGGTTACTGCCAGTTGAATCTG | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N1 probe | FAM—ACCCCGCATTACGTTTGGTGGACC—BHQ1 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N1 synthetic RNA target | rGrArCrCrCrCrArArArArUrCrArGrCrGrArArArUrGrCrArCrCrCrCrGrCrArUrUrArCrGrUrUrUrGrGrUrGrGrArCrCrCrUrCrArGrArUrUrCrArArCrUrGrGrCrArGrUrArArCrCrArGrA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N2 forward primer | TTACAAACATTGGCCGCAAA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N2 reverse primer | GCGCGACATTCCGAAGAA | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N2 probe | Cy5—ACAATTTGCCCCCAGCGCTTCAG—BHQ2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
N2 synthetic RNA target | rUrUrArCrArArArCrArUrUrGrGrCrCrGrCrArArArUrUrGrCrArCrArArUrUrUrGrCrCrCrCrCrArGrCrGrCrUrUrCrArGrCrGrUrUrCrUrUrCrGrGrArArUrGrUrCrGrCrGrC |
![]() | ||
Fig. 2 Theoretical PCR copy number plotted as a function of cycle (blue) with annealing temperature calculated using eqn (3) (red). Annealing temperature remains at 60.3 °C at the extremes, but drops to 57.4 °C around cycle 27. |
Similarly, as the ratio of quencher to fluorophore strands increases, the anneal switch temperature also increases (Fig. 5). The last ten cycles average anneal switch temperatures are shown as a function of the ratio of the two strands ([C1]/[C2]) at a fixed total concentration for each ratio ([C1] + [C2] = 500 nM). Results are consistent with literature, where melt temperatures increase with the ratio of the excess strand to the limiting strand.15Eqn (3) is plotted as a function of ratio with ΔH and ΔS values fitted from these trials to show the overall trend in the data (blue). The orange line indicates the theoretical annealing switch temperature if the ratio approaches infinity for a constant 500 nM concentration of L-DNA. The ratio of L-DNA analogs used in the rest of this report ([C1]/[C2] = 2.5) is indicated with a black arrow. The black arrows in both Fig. 4 and 5 correspond to an equivalent DNA total concentration and ratio of 500 nM, and [C1]/[C2] = 2.5, respectively.
![]() | ||
Fig. 5 Measured anneal switch temperature as a function of ratio of L-DNA quencher strand to fluorophore strand (red circles, mean ± s.d., N = 4). Eqn (3) with ΔH and ΔS calculated from the experimental data shows the overall trend of the data (dashed blue line). The 2.5 ratio used for the total concentration experiments also results in a switch temperature of 59.6 °C (black dashed line and arrow). The limit of the switch temperature as ([C1]/[C2]) approaches infinity for a fixed total concentration of 500 nM is 60.3 °C (dashed orange line). |
The data collected in these experiments were combined and used to calculate empirical ΔH and ΔS values for the primer model strand (see ESI for methodology†). Using these constants and eqn (3), a heat map of theoretical annealing temperature as a function of both total concentration and ratio of strands was created (Fig. 6). Theoretical annealing temperature is constant in arcs that come down from high concentrations and extend to high ratios, with steeper temperature gradients seen at lower concentrations and ratios, as shown by the faster color changes and closer grouping of the black isolines. All 8 sample groups from the ratio and concentration experiments are plotted on the heatmap to show the part of the graph within the scope of experimental data. The 59.6 °C temperature indicated with the arrows in Fig. 4 and 5 is shown at the intersection of the dashed lines that connect the experimental data.
However, for traditional PCR methods the previously observed failure18 of the N2 reaction in RT-PCR (without sample preparation) was consistent with previous research.17,18 The N2 reaction completely failed in nasopharyngeal matrix with a 55 °C annealing temperature and had a Cq delay > 20 in 35 mM NaCl at 55 °C, reinforcing that the SARS-CoV-2 N2 reaction is sensitive to background contaminant interference (Fig. 7, bottom panel). In all cases, identical unextracted samples returned a false negative result when performed according to the CDC SARS-CoV-2 EUA. The N1 positive control showed consistent Cq values in all samples for both the L-DNA control algorithm and traditional PCR methods, with small Cq delays in some groups but no complete failures (see ESI† for adaptive PCR N1 and a comparison of traditional PCR N2 data for a 61 °C annealing temperature).
Total DNA concentration experiments confirmed that total concentration of L-DNA should be selected carefully to best mimic the annealing behavior of D-DNA primers. The annealing temperature of primers and targets increases logarithmically with total concentration of complementary strands, meaning a mismatch in L-DNA and D-DNA total concentration would cause a similar mismatch in the annealing kinetics of the strands (Fig. 4). From a practical standpoint, while the concentration of the D-DNA primer is known, it is impossible to know how many copies of the D-DNA target sequence are in a real-world sample. However, it is safe to assume that the primer concentrations are in great excess of the target, so the total L-DNA concentration can be set equal to the total concentration of the D-DNA primer as a good approximation of total D-DNA complementary strand concentration. As an example, in our N1 and N2 experiments, there were 6.02 × 1012 primer copies per sample, versus only 2 × 105 target copies (Fig. 7). Moreover, since each primer consumed by the PCR process is extended to become one target strand, the total D-DNA complementary strand concentration does not change from cycle to cycle, so this approximation is equally valid throughout the reaction.
In addition to matching the total L-DNA concentration to the D-DNA primer concentration, the ratio of L-DNA strands should be set as high as is practical to ensure a good approximation of the exponential decrease of ratio between primers and targets in PCR (Fig. 5). Our data suggests that a ratio of 1:
2.5 (F
:
Q) works well (Fig. 7, for example), but because D-DNA primer to amplicon strand ratios change with each PCR cycle, a more detailed examination was performed to identify the cycles of a PCR reaction in which L-DNA hybridization state best mirrors the state of the D-DNA primer-target annealing. Because total concentration of L-DNA is matched to that of L-DNA, a large increase in strand ratio of quencher to fluorophore reduces the concentration of the fluorescently labeled strand to undetectable levels, which limits experimental testing. However, it is possible to use the kinetic constants derived from the experiment and eqn (3) to get a qualitative picture of the effects of strand ratio on annealing temperature over the entire cycle (Fig. 2). Although preset temperatures and times for control of PCR conditions assume that the annealing temperature does not change with cycle, the Van't Hoff theory predicts that the ideal annealing temperature changes across the cycles of a PCR reaction. At the two extremes (Cprimer/Camplicon approaches infinity and Camplicon/Cprimer approaches infinity), the primer annealing temperature is 60.3 °C (Fig. 5). In practice, the ratio of L-DNA components cannot approach infinity and practical considerations like fluorescence strength still need to be met.
While the annealing temperature between the extremes is difficult to predict, the amplicon and primer copy number estimates from a simple PCR model were used in the Van't Hoff equation to estimate the annealing temperature for each cycle and compared to the constant value of the L-DNA analogs. Models leading up to the Cq value are plentiful, but those that include the plateau phase are less common and use various explanations of the plateau phase in late PCR. Two of the primary explanations are primer exhaustion, and polymerase inhibition from overabundance of double-stranded amplicon. The simple model used here assumes that primer exhaustion is the cause of the PCR plateau phase because it has the most extreme ratio change of the commonly proposed plateau phase models. However, the choice of model is not critical as long as it demonstrates the phases of the PCR reaction, and a simplistic one with the largest possible ratio change was chosen for demonstration purposes. Eqn (3) was used with a PCR model based on this theory to calculate primer-amplicon annealing temperature as a function of PCR cycle (Fig. 2, red line, and Fig. 8, numbers). As seen from the theoretical data, the primer annealing temperature stays constant for most of the reaction, only differing for a few cycles in the midst of the exponential phase where it falls to 57.4 °C. This could have interesting implications for traditional PCR, as current methodologies typically do not vary the annealing temperature between cycles. While a potentially higher efficiency could be gained in the exponential phase of the reaction by accounting for this phenomenon, it is unlikely to produce large differences in outcomes as it occurs after Cq values are determined. Moreover, without knowing the cycle range of the exponential phase ahead of time, preset temperatures for each cycle would be difficult to set.
In terms of the L-DNA controlled approach, the practical experimental strand ratio of 2.5 times the amount of quencher as fluorophore produces a 0.7 °C underestimate in the L-DNA annealing temperature when compared to the D-DNA annealing temperature for most of the reaction (Fig. 5). Although it is unclear if this is an important difference, it could be reduced by either increasing the L-DNA concentration or increasing the quencher to fluorophore ratio. Compensating for the deviation during the exponential phase would be more difficult. However, because it occurs briefly and late in PCR cycles, after a Cq can be determined, correcting for it may not be necessary. In any event, traditional PCR cycle control based on fixed times and temperatures does not compensate for this deviation either. Thus, the ideal constant annealing temperature to aim for is the extreme case, given the sensitivity of the reaction in the pre-exponential phase.
There are some practical limitations of these potential L-DNA modifications. Increasing the total concentration will require more L-DNA per reaction, increasing reagent cost. Increasing the ratio of quencher to fluorophore while keeping total concentration constant, on the other hand, will diminish the fluorescence signal necessary for the control algorithm to function. The quickest method of calculating an L-DNA anneal sensor concentration is to match the total concentration of primers, then use the highest possible strand ratio while maintaining good fluorescence signal. This method is how the L-DNA implementation used in this report was calculated, which has the 0.7 °C underestimate mentioned above. If a more precise estimate is desired, ΔH and ΔS can be obtained either experimentally or calculated and a heatmap like Fig. 8 can be created to find the ideal concentration and ratio to match the D-DNA primers and amplicons. As seen in the figure and predicted by theory, the annealing temperature for a given total concentration approaches a limit as the ratio of strands approaches infinity. Therefore, a more precise estimate for early PCR cycles can be calculated from this chart by going straight across from the total primer concentration to the right, then following along the isoline back to a detectable fluorescence that emulates the extreme ratios present for most of the PCR reaction. The bold isoline at 60.3 °C in Fig. 8 shows where this would be done for the experiments in this report, following it back from the right and out of the tinted, undetectable region on the right of the figure.
In terms of a practical demonstration, applying these findings to the SARS-CoV-2 N2 reaction by using them to inform the selected L-DNA annealing sensor concentration and strand ratio showed an insignificant amount of performance loss in even unextracted samples (Fig. 7, top panel), while the traditional PCR entirely failed using published CDC procedure (Fig. 7, bottom panel). The hybridization-controlled PCR produced positive results for all positive samples with no adjustment or calibration necessary, “adapting” the length of its cooling cycle—and thus the annealing temperature—to the change in sample background. Some small delays from the water controls were seen in both N1 and N2, none of which were statistically significant, and inconsequential in comparison to the 20 or more cycle delay in the N2 samples performed in a standard fixed cycle PCR instrument. This delay can likely be attributed to the CDC's prescribed annealing temperature of 55 °C already being below the optimal annealing temperature for the N2 reaction in an extracted sample, which IDT's web tools indicates should be around 57.6 °C (Tm – 5 °C). The CDC's choice of annealing temperature was likely chosen by the multiplexed nature of the original assay, and that it worked well with the sample preparation procedures in their EUA. It did not work well when performed in unextracted nasopharyngeal samples. However, since these salts affect L-DNA and D-DNA hybridization equally, controlling the heating and cooling cycles using the L-DNA fluorescence shifts to optimize primer-target annealing.
While this approach overcomes limitations in standard PCR, the adaptive instrument does have its own practical challenges. One primary limitation of the adaptive instrument is that it can only be tuned for one set of primers in a multiplexed reaction. In this case, for example, the adaptive instrument based thermal cycling on N2 L-DNA and was not tuned to N1. The N2 reaction was chosen as it was found to be the more sensitive to annealing temperature in prior work.18 Choosing the most sensitive reaction allows that sequence to control the critical annealing phase, and is recommended as a simple way of deciding which sequence the L-DNA analogs should mirror. It is important to note that the L-DNA controlled approach does not correct for all background interferents. Direct polymerase inhibition by background molecules such as hemoglobin will not be accounted for by a hybridization control mechanism.24 Similarly, substances that affect fluorescent dye reporting25 and stereospecific molecules such as proteins that bind to D-DNA26 will not affect the biologically inert, end-labeled L-DNA and thus will not be compensated for. This approach primarily compensates for kinetic interference by common background components like salts and alcohols, as well as instrumentation inconsistencies. Finally, use of the L-DNA control method requires using two of the limited number of fluorescent channels available on the instrument for cycling control, making them unavailable for PCR. While we have previously reported using a single channel2 to monitor annealing and melting, the two-channel approach reported here was used for greater precision and cycling reliability for these experiments. Improvements to the instrument and control algorithm design (to be discussed in a manuscript in preparation) should reclaim these channels and allow greater multiplexing in these reactions.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ay00083h |
This journal is © The Royal Society of Chemistry 2024 |