Developing a Machine-Learning ‘Smart’ PCR Thermocycler, Part 1: Construction of a Theoretical Framework
Abstract
:1. Introduction
- (1)
- Defining a goal for PCR ‘effectiveness’.
- (2)
- Accessing and controlling a PCR thermocycler in a real-time interactive manner.
- (3)
- Carrying out a PCR in a way that provides reliable measurable real-time feedback for an algorithm to use.
- (4)
- Creating a metric that represents the quality of the profile.
- (5)
- Weighing profile quality against the goal.
- (6)
- Carrying out machine learning on a set of training data to inform an algorithm for use in the smart PCR system.
2. Theory
2.1. Defining a Goal for PCR ‘Effectiveness’
- peaks within an optimal height range (measured in relative fluorescence units, rfu);
- More complete DNA profiles;
- Better balance between peaks within a locus;
- Better balance between peaks at different loci;
- Fewer artefacts being generated;
- Less prominent artefacts, such as lower, or fewer stutter peaks.
2.2. Accessing and Controlling a PCR Thermocycler in a Real-Time Interactive Manner
- (1)
- Set up the initial cycle(s) of the PCR program with default starting parameters, using various Chai API endpoints to modify experiments, stages and steps. Note: due to systems having a limited sensitivity to DNA concentration, the number of cycles run initially before any intervention is likely to be much larger than once the concentration has exceeded the threshold for detection.
- (2)
- Start a cycle running on the instrument using the “device/start” endpoint in the Chai API.
- (3)
- Retrieve the fluorescence amplification data at the end of the cycle using the “amplification_data” API endpoint.
- (4)
- Pass the retrieved amplification data to an external algorithm that determines the optimal conditions of the next PCR cycle(s).
- (5)
- Set up the next cycle(s) on the instrument with the algorithm-determined parameters using the Chai API, as before.
- (6)
- Continue through steps 2 to 5 until either the maximum number of cycles are run, or the early termination criteria are met.
- (7)
- End the program and write out the PCR conditions that were used for each cycle.
2.3. Carrying Out a PCR in a Way That Provides Actionable Real-Time Feedback
- (A)
- For each DNA sample being amplified, run the endpoint PCR and a qPCR (in separate tubes) at the same time, and monitor the real-time feedback of both tubes.
- (B)
- Create a single reaction that allows real-time feedback from the endpoint PCR. For example, the creation of a combination reaction that is essentially a mixture of GlobalFiler (Thermo Fisher Scientific) and Quantiplex Pro (QIAGEN).
2.4. Creating a Metric That Represents the Quality of the Profile
- (A)
- A component that deals with peak height. Ideally, peak heights in a DNA profile will be high enough so that they are not at risk of dropping out, but not so high that they start to cause significant pull-up artefacts (and, if pushed even further, not so high that they saturate the capillary electrophoresis detection system). To achieve this, we set an ideal peak height and the variation that would be tolerated around that ideal height. Practically, this was realised by calculating the probability density function of the measured peak height based on the ideal peak height and permitted standard deviation from that ideal peak height. A score was then calculated based on the log10 of the density of the exponential distribution at that point. The use of the logarithm ensured the decrease in score was not too severe, with height scores remaining higher in response to variations in peak height than if it were not utilised. Since the probability density function varies between 0 and 1, the logarithm was always negative. Furthermore, the probability density function was maximal, but not 1, at the ideal peak height, meaning that the logarithm of the probability density function was always negative. This resulted in an offset, where there was always a cost associated with any measured height, even the ideal value. This offset was removed (by adding a constant), such that the score associated with obtaining the ideal peak height was 0, with decreasing scores (larger negative values) related to the further away the measured height was from this ideal value.
- (B)
- A component that deals with peak balance. We chose a method that was intended to capture multiple manifestations of peak height variability. The metric was based on all peak heights in the profile (with missing peaks assigned a value of 0). This way, peak imbalance within a locus, between loci, or dropped-out alleles/loci would all be accounted for. The metric calculated the standard deviation of the peak heights and then divided this by the mean of the peak heights, to obtain the coefficient of variation (COV). The COV was used instead of the standard deviation to prevent the correlation between peak height and standard deviation always driving the metric to prefer lower peak heights. Unlike the first component (peak heights), there is no ideal amount of peak height variability, other than ideally having no peak height variability or imbalance. Therefore, we modelled the COV with an exponential distribution, so that the smaller the peak height variability the less the profile would be penalised. There is no specific amount by which to penalise peak height variability, except that it must be balanced with the peak height component. If the parameter of the exponential distribution was chosen to be too high, then the peak balance component would dominate the metric, and if it were too low, then the peak height component would dominate the metric (and it would become too tolerant of peak height variability). Figure 1 shows some combinations of peak height and peak imbalance that utilise these combinations of parameters. As with component A, the peak height variability component was assigned a score based on the log10 of the density of the exponential distribution at that point. Once again, an ideal value was 0, with less desirable outcomes resulting in increasingly negative scores.
- (C)
- A component that deals with process duration. The time it takes to run the entire procedure is an important consideration. Reducing the time taken to obtain a result is of benefit, as it means a more efficient process and additional throughput. However, care should be taken to not unduly emphasise duration at the expense of the quality of the resulting product. We decided to increase the cost in proportion to the duration of the process, specifically the total time of the denaturing and annealing cycles. Since this was but one factor, and it was added to the others, even a very high score (i.e., close to 0) would not be sufficient to overcome poor peak height and COV scores. However, it would be sufficient to influence the selection of a faster process that produced a result of acceptable quality.
- (D)
- A component that deals with artefacts. Machine-learning algorithms are known to achieve goals by finding solutions that have consequences not originally envisaged by humans [36]. For example, a DNA profile that achieved high scores in both component A and B could still be largely useless. Imagine that a machine-learning algorithm learned to suggest a set of PCR cycling conditions that lead to the presence of peaks at every allelic position (much like an allelic ladder). As long as those peaks were around 5000 relative fluorescence units (rfu), and all of similar height, this would receive a high score. However, the profile itself would be largely useless in the context of identifying the source of the DNA, due to being comprised almost entirely of artefacts. Therefore, it is likely that the profile metric will need to include an artefact component. The same as with point B), there is no ideal amount (or number) of artefacts other than none, and so an exponential distribution is likely to be appropriate. The variate being modelled by the exponential distribution could be the summed rfu of the artefact peaks, or the number of artefact peaks. In our initial work, artefacts were not observed (note that we do not count stutters as artefacts, as these occur in all programs, but a model could be set that took stutter ratios into account if this were desired by a user) and so no artefact component was added to the metric, but will likely be required as work continues. The exponential distribution parameter will have to be chosen as before, so that the presence of artefacts would be balanced against the other components. We note that there are potential difficulties associated with the incorporation of an artefact penalty, particularly when dealing with complex, mixed profiles, and when considering low analytical thresholds. Even when the ground truth is known, there may be additional peaks that arise as drop-in, which are legitimate (albeit unwanted) amplifications which perhaps should not be considered within a drop-in penalty. We suspect the way forward would be to penalize any peaks that do not align with expectation and to conduct multiple repeats for any PCR cycling conditions trialled, so that the effects of a sporadic amplification in one repeat would be minimized, as it was spread across replicates.
2.5. Weighing Profile Quality against the Goal
- is the mean of all observed peaks.
- is the probability density function at the point for the distribution with mean (i.e., the ideal or reference mean value) and standard deviation (i.e., the value for weighting variations from the ideal).
- is the constant offset to ensure an ideal peak height achieved a score of 0.
- is the exponential distribution at the point with coeficient .
- is the coefficient of variation in the peaks.
- is the number of observed artefact peaks.
- t is the time (in minutes) the PCR program takes to complete.
- K parameters weigh the importance of each element of the score. Note: while probabilities are between 0 and 1, depending on the selected value of , it is possible for a probability density to be greater than 1, meaning not all logarithmic responses will be less than or equal to zero. However, the inclusion of the constant C will ensure a maximum value of 0. This means values from both probability density scoring components will always be less negative, while the number of artefacts and the duration of the process is always positive. To ensure a more negative score indicates a response that is less desirable, all elements of the profile score function were required to be negative. Therefore, K0 and K1 values are positive, while K2 and K3 must be negative.
2.6. Carrying Out Machine Learning on a Set of Training Data to Inform an Algorithm for Use in the Smart PCR System
2.6.1. Open-Loop Optimisation
- (1)
- A learning rate is selected. This value must be less than 1 (otherwise it will be unstable) and could be fixed or decaying (where the value decreases over the number of iterations), depending on the number of iterations required. The larger the number of iterations, the more beneficial a decaying learning rate would be.
- (2)
- A group (swarm) of (semi-)random input parameters (each called a particle) are generated within the known constraints of the system.
- (3)
- PCR cycles are run with parameters specified by each of the particles.
- (4)
- The quality/score/fitness of the outcomes of each of these particles is calculated.
- (5)
- The distance between a particle and all the others is calculated in the parameter space.
- (6)
- The movement for a particular particle (i.e., the difference between the current and new testing parameters) is determined by adding together the respective fitness divided by the relative distance to each other particle in the swarm and scaling by the learning rate.
- (7)
- The new parameters for each of the particles are determined.
- (8)
- Steps (3) to (7) are then repeated, until the particles converge on a solution.
2.6.2. Closed-Loop Optimisation
3. Methods
3.1. Ethics Approval
3.2. Control DNA
3.3. DNA Amplification and STR Profiling
3.3.1. Altering PCR Cycling Conditions for Trace Samples
3.3.2. Priming qPCR Targets before Altering PCR Cycling Conditions to Improve DNA Amplification of Trace Samples
3.3.3. Altering qPCR Cycling Conditions to Improve Amplification Efficiency
3.4. Data Analysis
3.4.1. STR Data
3.4.2. Quantification Data
- Y = modelled output fluorescence;
- X = cycle number or time;
- A = amplitude of final fluorescence value;
- B = gradient of the response;
- C = midpoint of the fluorescence response (in either cycle number or time).
4. Results and Discussion
4.1. Altering PCR Cycling Conditions for Trace Samples—No qPCR Priming
4.2. Priming qPCR Targets before Altering PCR Cycling Conditions to Improve DNA Amplification of Trace Samples
4.3. Altering qPCR Cycling Conditions to Improve Amplification Efficiency
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Program | Initial Hold | Cycling Conditions (×30 Cycles) | Final Hold | |
---|---|---|---|---|
Denaturation Step | Annealing/Extension Step | |||
Standard GlobalFilerTM manufacturer’s protocol | 94 °C, 3 min | 94 °C, 10 s | 59 °C, 90 s | 60 °C, 10 min |
Modified GlobalFilerTM protocol | 94 °C, 3 min | 94 °C, 10 s | 59 °C, 60 s (+1.56 per cycle) | 60 °C, 10 min |
Program | Initial Hold | Cycling (×16 Cycles) | Initial Hold | Cycling (×30 Cycles) | Final Hold | ||
---|---|---|---|---|---|---|---|
D | A/E | D | A/E | ||||
Standard GlobalFilerTM manufacturer’s protocol | 95 °C, 3 min | 94 °C, 5 s | 60 °C, 10 s | 94 °C, 3 min | 94 °C, 10 s | 59 °C, 90 s | 60 °C, 10 min |
Modified GlobalFilerTM protocol | 95 °C, 3 min | 94 °C, 5 s | 60 °C, 10 s | 94 °C, 3 min | 94 °C, 10 s | 59 °C, 60 s (+1.56 s) | 60 °C, 10 min |
Program | Initial Hold | Standard Cycling (×16 Cycles) | Altered Cycling (×24 Cycles) | ||
---|---|---|---|---|---|
D | A/E | D | A/E | ||
Standard Investigator Quantiplex Pro RGQ manufacturer’s protocol | 95 °C, 3 min | 95 °C, 5 s | 60 °C, 10 s | 95 °C, 5 s | 60 °C, 10 s |
Altered annealing/extension qPCR program 1 (AEQ1) | 95 °C, 3 min | 95 °C, 5 s | 60 °C, 10 s | 95 °C, 5 s | 60 °C, 30 s |
Altered annealing/extension qPCR program 2 (AEQ2) | 95 °C, 3 min | 95 °C, 5 s | 60 °C, 10 s | 95 °C, 5 s | 60 °C, 50 s |
Altered annealing/extension qPCR program 3 (AEQ3) | 95 °C, 3 min | 95 °C, 5 s | 60 °C, 10 s | 95 °C, 5 s | 60 °C, 70 s |
Altered annealing/extension qPCR program 4 (AEQ4) | 95 °C, 3 min | 95 °C, 5 s | 60 °C, 10 s | 95 °C, 5 s | 60 °C, 90 s |
PCR Program | Average Number of Observed Alleles | Average Percent Allele Loss (%) | Average Sub-Source Likelihood Ratio |
---|---|---|---|
Standard GlobalFilerTM manufacturer’s protocol | 34 | 9.73 | 8.86 × 1023 (9.04 × 1017–4.04 × 1024) |
Primed standard GlobalFilerTM manufacturer’s protocol | 21 | 43.78 | 3.61 × 1017 (7.77 × 102–1.80 × 1018) |
Modified GlobalFilerTM protocol | 32 | 13.51 | 3.65 × 1020 (2.97 × 1015–1.82 × 1021) |
Primed modified GlobalFilerTM protocol | 13 | 65.41 | 3.34 × 1016 (6.00 × 10−4–1.67 × 1017) |
PCR Program | Average Peak Heights (RFU) | Average Penalties | Average Profile Quality Score | ||||
---|---|---|---|---|---|---|---|
Mean | Std. Dev. | COV | Peak Height | COV | Artefacts | ||
Standard GlobalFilerTM manufacturer’s protocol | 687 | 631 | 0.92 | −7.44 | −2.00 | 0 | −12.84 |
Primed standard GlobalFilerTM manufacturer’s protocol | 145 | 287 | 2.05 | −8.52 | −4.46 | −7.6 | −23.58 |
Modified GlobalFilerTM protocol | 436 | 421 | 0.97 | −7.93 | −2.11 | 0 | −13.44 |
Primed modified GlobalFilerTM protocol | 61 | 119 | 2.24 | −8.70 | −4.86 | −5.2 | −20.15 |
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McDonald, C.; Taylor, D.; Masawi, G.M.; Khan, A.K.A.; Leibbrandt, R.; Linacre, A.; Brinkworth, R.S.A. Developing a Machine-Learning ‘Smart’ PCR Thermocycler, Part 1: Construction of a Theoretical Framework. Genes 2024, 15, 1196. https://doi.org/10.3390/genes15091196
McDonald C, Taylor D, Masawi GM, Khan AKA, Leibbrandt R, Linacre A, Brinkworth RSA. Developing a Machine-Learning ‘Smart’ PCR Thermocycler, Part 1: Construction of a Theoretical Framework. Genes. 2024; 15(9):1196. https://doi.org/10.3390/genes15091196
Chicago/Turabian StyleMcDonald, Caitlin, Duncan Taylor, Gershom Mwachari Masawi, Ayesha Khalid Ahmed Khan, Richard Leibbrandt, Adrian Linacre, and Russell S. A. Brinkworth. 2024. "Developing a Machine-Learning ‘Smart’ PCR Thermocycler, Part 1: Construction of a Theoretical Framework" Genes 15, no. 9: 1196. https://doi.org/10.3390/genes15091196