Title:

Kind
Code:

A1

Abstract:

A computer program product for determining a threshold value (e.g., a threshold cycle number or time value) in a nucleic acid amplification reaction tangibly embodies instructions readable by a machine to perform the steps of deriving a growth curve from measurements of a signal whose intensity is related to a quantity of nucleic acid sequence being amplified in the reaction, calculating a derivative of the growth curve, identifying a characteristic of the derivative, and determining a threshold value associated with the characteristic of the derivative. The method provides for highly reproducible threshold values that are independent of noise or background signal in the amplification reaction. Embodiments of a computer program product for determining a starting quantity of a nucleic acid sequence in a test sample are also provided.

Inventors:

Mcmillan, William A. (Cupertino, CA, US)

Christel, Lee A. (Palo Alto, CA, US)

Borkholder, David A. (San Jose, CA, US)

Young, Steven J. (Los Gatos, CA, US)

Christel, Lee A. (Palo Alto, CA, US)

Borkholder, David A. (San Jose, CA, US)

Young, Steven J. (Los Gatos, CA, US)

Application Number:

10/702538

Publication Date:

05/20/2004

Filing Date:

11/05/2003

Export Citation:

Assignee:

Cepheid (Sunnyvale, CA)

Primary Class:

Other Classes:

702/19

International Classes:

View Patent Images:

Related US Applications:

Primary Examiner:

KIM, YOUNG J

Attorney, Agent or Firm:

Kilpatrick Townsend & Stockton LLP - West Coast (Atlanta, GA, US)

Claims:

1. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring at a plurality of different times during a nucleic acid amplification reaction at least one signal whose intensity is related to a quantity of a nucleic acid sequence being amplified in the reaction, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) deriving a growth curve from measurements of the signal; b) calculating a derivative of the growth curve; c) identifying a characteristic of the derivative; and d) determining a cycle number associated with the characteristic of the derivative.

2. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

3. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

4. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

5. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

6. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different cycles in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the cycle number associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the cycle number as the location, in cycles, of a peak of the second order curve.

7. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring at a plurality of different times during a nucleic acid amplification reaction at least one signal whose intensity is related to a quantity of a nucleic acid sequence being amplified in the reaction, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) deriving a growth curve from the measurements of the signal; b) calculating a derivative of the growth curve; c) identifying a characteristic of the derivative; and d) determining a time value associated with the characteristic of the derivative.

8. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

9. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

10. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

11. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

12. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a plurality of different measurement times in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the time value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the time value as the location of a peak of the second order curve.

13. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring signals indicative of the quantities of a target nucleic acid sequence being amplified in a test sample, containing an unknown starting quantity of the target nucleic acid sequence, and of a calibration nucleic acid sequence being amplified in a plurality of calibration samples, containing respective known starting quantities of the calibration nucleic acid sequence, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) determining a respective threshold value for the target nucleic acid sequence in the test sample and for each of the known starting quantities of the calibration nucleic acid sequence in the calibration samples, wherein each threshold value is determined for a nucleic acid sequence in a respective sample by: i) deriving a growth curve for the nucleic acid sequence from the measured signals; ii) calculating a derivative of the growth curve; iii) identifying a characteristic of the derivative; and iv) determining the threshold value associated with the characteristic of the derivative; b) deriving a calibration curve from the threshold values determined for the known starting quantities of the nucleic acid sequence in the calibration samples; and c) determining the starting quantity of the target nucleic acid sequence in the test sample using the calibration curve and the threshold value determined for the target sequence.

14. The computer program product of claim 13, wherein each of the threshold values comprises a cycle number.

15. The computer program product of claim 13, wherein each of the threshold values comprises an elapsed time of amplification.

16. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

17. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

18. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

19. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

20. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different measurement points in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the threshold value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the threshold value as the location of a peak of the second order curve.

21. A computer program product readable by a machine having at least one detection mechanism for measuring: i) signals indicative of the respective quantities of a target nucleic acid sequence in a test sample and of a first internal control being amplified in a first nucleic acid amplification reaction, wherein the first internal control comprises a second nucleic acid sequence different than the target nucleic acid sequence in the test sample; ii) signals indicative of the respective quantities of a first standard and of a second internal control being amplified in a second nucleic acid amplification reaction, wherein the first standard comprises a first known starting quantity of a calibration nucleic acid sequence different than the second nucleic acid sequence, and wherein the second internal control comprises the second nucleic acid sequence; iii) signals indicative of the respective quantities of a second standard and of a third internal control being amplified in a third nucleic acid amplification reaction, wherein the second standard comprises a second known starting quantity of the calibration nucleic acid sequence, the third internal control comprises the second nucleic acid sequence, and the starting quantity of the second nucleic acid sequence is substantially the same in each of the amplification reactions; wherein the computer program product embodies a program of instructions executable by the machine to perform the steps of: a) determining a respective threshold value for each of the standards, each of the internal controls, and the target nucleic acid sequence in the test sample; b) normalizing the threshold value determined for the target nucleic acid sequence in the test sample to the threshold value determined for the first internal control; c) normalizing the threshold values determined for the first and second standards to the threshold values determined for the second and third internal controls, respectively; d) deriving a calibration curve from the known starting quantities and the normalized threshold values of the first and second standards; and e) determining the starting quantity of the target nucleic acid sequence in the test sample using the calibration curve and the normalized threshold value determined for the target sequence.

22. The computer program product of claim 21, wherein each of the threshold values comprises a cycle number.

23. The computer program product of claim 21, wherein each of the threshold values comprises an elapsed time of amplification.

24. The computer program product of claim 21, wherein a respective threshold value is determined for a nucleic acid sequence by: i) deriving a growth curve from the measured signals; ii) calculating a derivative of the growth curve; iii) identifying a characteristic of the derivative; and iv) determining the threshold value associated with the characteristic of the derivative.

25. The computer program product of claim 24, wherein the threshold value comprises a cycle number.

26. The computer program product of claim 24, wherein the threshold value comprises an elapsed time of amplification.

27. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

28. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

29. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

30. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

31. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different measurement points in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the threshold value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the threshold value as the location of a peak of the second order curve.

32. The computer program product of claim 21, wherein the step of normalizing the threshold value determined for the target nucleic acid sequence in the test sample to the threshold value determined for the first internal control comprises dividing the threshold value determined for the target nucleic acid sequence by the threshold value determined for the first internal control.

33. The computer program product of claim 21, wherein the step of normalizing the threshold values determined for the first and second standards to the threshold values determined for the second and third internal controls, respectively, comprises dividing the threshold values determined for the first and second standards by the threshold values determined for the second and third internal controls, respectively.

34. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring signals indicative of the respective quantities of a first nucleic acid sequence, a first standard, and a second standard being amplified in a reaction vessel, wherein the first standard comprises a known starting quantity of a second nucleic acid sequence different than the first nucleic acid sequence, and wherein the second standard comprises a known starting quantity of a third nucleic acid sequence different than the first and second sequences, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) determining a respective threshold value for the first nucleic acid sequence, first standard, and second standard; b) deriving a calibration curve from the known starting quantities and from the threshold values determined for the first and second standards; and c) determining the starting quantity of the first nucleic acid sequence in the test sample using the calibration curve and the threshold value determined for the first nucleic acid sequence.

35. The computer program product of claim 34, wherein each of the threshold values comprises a cycle number.

36. The computer program product of claim 34, wherein each of the threshold values comprises an elapsed time of amplification.

37. The computer program product of claim 34, wherein a respective threshold value is determined for each nucleic acid sequence by: i) deriving a growth curve from the measurements of the signals; ii) calculating a derivative of the growth curve; iii) identifying a characteristic of the derivative; and iv) determining the threshold value associated with the characteristic of the derivative.

38. The computer program product of claim 37, wherein the threshold value comprises a cycle number.

39. The computer program product of claim 37, wherein the threshold value comprises an elapsed time of amplification.

40. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

41. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

42. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

43. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

44. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different measurement points in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the threshold value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the threshold value as the location of a peak of the second order curve.

2. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

3. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

4. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

5. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

6. The computer program product of claim 1, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different cycles in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the cycle number associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the cycle number as the location, in cycles, of a peak of the second order curve.

7. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring at a plurality of different times during a nucleic acid amplification reaction at least one signal whose intensity is related to a quantity of a nucleic acid sequence being amplified in the reaction, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) deriving a growth curve from the measurements of the signal; b) calculating a derivative of the growth curve; c) identifying a characteristic of the derivative; and d) determining a time value associated with the characteristic of the derivative.

8. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

9. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

10. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

11. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating the first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

12. The computer program product of claim 7, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a plurality of different measurement times in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the time value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the time value as the location of a peak of the second order curve.

13. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring signals indicative of the quantities of a target nucleic acid sequence being amplified in a test sample, containing an unknown starting quantity of the target nucleic acid sequence, and of a calibration nucleic acid sequence being amplified in a plurality of calibration samples, containing respective known starting quantities of the calibration nucleic acid sequence, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) determining a respective threshold value for the target nucleic acid sequence in the test sample and for each of the known starting quantities of the calibration nucleic acid sequence in the calibration samples, wherein each threshold value is determined for a nucleic acid sequence in a respective sample by: i) deriving a growth curve for the nucleic acid sequence from the measured signals; ii) calculating a derivative of the growth curve; iii) identifying a characteristic of the derivative; and iv) determining the threshold value associated with the characteristic of the derivative; b) deriving a calibration curve from the threshold values determined for the known starting quantities of the nucleic acid sequence in the calibration samples; and c) determining the starting quantity of the target nucleic acid sequence in the test sample using the calibration curve and the threshold value determined for the target sequence.

14. The computer program product of claim 13, wherein each of the threshold values comprises a cycle number.

15. The computer program product of claim 13, wherein each of the threshold values comprises an elapsed time of amplification.

16. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

17. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

18. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

19. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

20. The computer program product of claim 13, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different measurement points in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the threshold value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the threshold value as the location of a peak of the second order curve.

21. A computer program product readable by a machine having at least one detection mechanism for measuring: i) signals indicative of the respective quantities of a target nucleic acid sequence in a test sample and of a first internal control being amplified in a first nucleic acid amplification reaction, wherein the first internal control comprises a second nucleic acid sequence different than the target nucleic acid sequence in the test sample; ii) signals indicative of the respective quantities of a first standard and of a second internal control being amplified in a second nucleic acid amplification reaction, wherein the first standard comprises a first known starting quantity of a calibration nucleic acid sequence different than the second nucleic acid sequence, and wherein the second internal control comprises the second nucleic acid sequence; iii) signals indicative of the respective quantities of a second standard and of a third internal control being amplified in a third nucleic acid amplification reaction, wherein the second standard comprises a second known starting quantity of the calibration nucleic acid sequence, the third internal control comprises the second nucleic acid sequence, and the starting quantity of the second nucleic acid sequence is substantially the same in each of the amplification reactions; wherein the computer program product embodies a program of instructions executable by the machine to perform the steps of: a) determining a respective threshold value for each of the standards, each of the internal controls, and the target nucleic acid sequence in the test sample; b) normalizing the threshold value determined for the target nucleic acid sequence in the test sample to the threshold value determined for the first internal control; c) normalizing the threshold values determined for the first and second standards to the threshold values determined for the second and third internal controls, respectively; d) deriving a calibration curve from the known starting quantities and the normalized threshold values of the first and second standards; and e) determining the starting quantity of the target nucleic acid sequence in the test sample using the calibration curve and the normalized threshold value determined for the target sequence.

22. The computer program product of claim 21, wherein each of the threshold values comprises a cycle number.

23. The computer program product of claim 21, wherein each of the threshold values comprises an elapsed time of amplification.

24. The computer program product of claim 21, wherein a respective threshold value is determined for a nucleic acid sequence by: i) deriving a growth curve from the measured signals; ii) calculating a derivative of the growth curve; iii) identifying a characteristic of the derivative; and iv) determining the threshold value associated with the characteristic of the derivative.

25. The computer program product of claim 24, wherein the threshold value comprises a cycle number.

26. The computer program product of claim 24, wherein the threshold value comprises an elapsed time of amplification.

27. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

28. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

29. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

30. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

31. The computer program product of claim 24, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different measurement points in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the threshold value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the threshold value as the location of a peak of the second order curve.

32. The computer program product of claim 21, wherein the step of normalizing the threshold value determined for the target nucleic acid sequence in the test sample to the threshold value determined for the first internal control comprises dividing the threshold value determined for the target nucleic acid sequence by the threshold value determined for the first internal control.

33. The computer program product of claim 21, wherein the step of normalizing the threshold values determined for the first and second standards to the threshold values determined for the second and third internal controls, respectively, comprises dividing the threshold values determined for the first and second standards by the threshold values determined for the second and third internal controls, respectively.

34. A computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring signals indicative of the respective quantities of a first nucleic acid sequence, a first standard, and a second standard being amplified in a reaction vessel, wherein the first standard comprises a known starting quantity of a second nucleic acid sequence different than the first nucleic acid sequence, and wherein the second standard comprises a known starting quantity of a third nucleic acid sequence different than the first and second sequences, the computer program product embodying a program of instructions executable by the machine to perform the steps of: a) determining a respective threshold value for the first nucleic acid sequence, first standard, and second standard; b) deriving a calibration curve from the known starting quantities and from the threshold values determined for the first and second standards; and c) determining the starting quantity of the first nucleic acid sequence in the test sample using the calibration curve and the threshold value determined for the first nucleic acid sequence.

35. The computer program product of claim 34, wherein each of the threshold values comprises a cycle number.

36. The computer program product of claim 34, wherein each of the threshold values comprises an elapsed time of amplification.

37. The computer program product of claim 34, wherein a respective threshold value is determined for each nucleic acid sequence by: i) deriving a growth curve from the measurements of the signals; ii) calculating a derivative of the growth curve; iii) identifying a characteristic of the derivative; and iv) determining the threshold value associated with the characteristic of the derivative.

38. The computer program product of claim 37, wherein the threshold value comprises a cycle number.

39. The computer program product of claim 37, wherein the threshold value comprises an elapsed time of amplification.

40. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a positive peak of the second derivative.

41. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a negative peak of the second derivative.

42. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a second derivative of the growth curve, and wherein the characteristic comprises a zero crossing of the second derivative.

43. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating a first derivative of the growth curve, and wherein the characteristic comprises a positive peak of the first derivative.

44. The computer program product of claim 37, wherein the step of calculating a derivative of the growth curve comprises calculating second derivative values of the growth curve at a number of different measurement points in the reaction to yield a plurality of second derivative data points, the characteristic comprises a positive peak of the second derivative, and the step of determining the threshold value associated with the positive peak comprises: i) fitting a second order curve to the second derivative data points; and ii) calculating the threshold value as the location of a peak of the second order curve.

Description:

[0001] This application is a division of U.S. application Ser. No. 09/562,195 filed May 1, 2000 which is incorporated by reference herein.

[0002] A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by any one of the patent disclosure as it appears in the U.S. Patent and Trademark Office patent files or records, but otherwise reserves all copyright rights whatsoever.

[0003] This invention relates to a computer program product for quantitative analysis of a nucleic acid amplification reaction.

[0004] Quantitative nucleic sequence analysis plays an increasingly important role in the fields of biological and medical research. For example, quantitative gene analysis has been used to determine the genome quantity of a particular gene, as in the case of the human HER-2 oncogene, which is amplified in approximately 30% of human breast cancers. Gene and genome quantitation have also been used in determining and monitoring the levels of human immunodeficiency virus (HIV) in a patient throughout the different phases of the HIV infection and disease. It has been suggested that higher levels of circulating HIV and failure to effectively control virus replication after infection may be associated with a negative disease prognosis. Accordingly, an accurate determination of nucleic acid levels early in an infection may serve as a useful tool in diagnosing illness, while the ability to correctly monitor the changing levels of viral nucleic acid in one patient throughout the course of an illness may provide clinicians with critical information regarding the effectiveness of treatment and progression of disease.

[0005] Several methods have been described for the quantitative analysis of nucleic acid sequences. The polymerase chain reaction (PCR) and reverse-transcriptase PCR (RT-PCR) permit the analysis of small starting quantities of nucleic acid (e.g., as little as one cell equivalent). Early methods for quantitation involved measuring PCR product at the end of temperature thermal cycling and relating this level to the starting DNA concentration. Unfortunately, the absolute amount of product generated does not always bear a consistent relationship to the amount of target sequence present at the initiation of the reaction, particularly for clinical samples. Such an endpoint analysis reveals the presence or absence of starting nucleic acid, but generally does not provide an accurate measure of the number of DNA targets. Both the kinetics and efficiency of amplification of a target sequence are dependent on the starting quantity of that sequence, and on the sequence match of the primers and target template, and may also be affected by inhibitors present in the sample. Consequently, endpoint measurements have very poor reproducibility.

[0006] Another method, quantitative competitive PCR (QC-PCR), has been developed and used widely for PCR quantitation. QC-PCR relies on the inclusion of a known amount of an internal control competitor in each reaction mixture. To obtain relative quantitation, the unknown target PCR product is compared with the known competitor PCR product, usually via gel electrophoresis. The relative amount of target-specific and competitor DNA is measured, and this ratio is used to calculate the starting number of target templates. The larger the ratio of target specific product to competitor specific product, the higher the starting DNA concentration. Success of a QC-PCR assay relies on the development of an internal control that amplifies with the same efficiency as the target molecule. However, the design of the competitor and the validation of amplification efficiencies require much effort. In the QC-PCR method of RNA quantitation, a competitive RNA template matched to the target sequence of interest, but different from it by virtue of an introduced internal deletion, is used in a competitive titration of the reverse transcription and PCR steps, providing stringent internal control. Increasing amounts of known copy numbers of competitive template are added to replication portions of the test sample, and quantitation is based on determination of the relative (not absolute) amounts of the differently sized amplified products derived from the wild-type and competitive templates, after electrophoretic separation.

[0007] In addition to requiring time-consuming and burdensome downstream processing such as hybridization or gel electrophoresis, these assays have limited sensitivity to a range of target nucleic acid concentrations. For example, in competitor assays, the sensitivity to template concentration differences may be compromised when either the target or added competitor DNA is greatly in excess of the other. The dynamic range of the assays that measure the amount of end product can also be limited in that the chosen number of cycles of some reactions may have reached a plateau level of product prior to other reactions. Differences in starting template levels in these reactions may therefore not be well reflected. Furthermore, small differences in the measured amount of product may result in widely varying estimates of the starting template concentration, leading to inaccuracies due to variable reaction conditions, variations in sampling, or the presence of inhibitors.

[0008] To reduce the amount of post-amplification analysis required to determine a starting nucleic acid quantity in a sample, additional methods have been developed to measure nucleic acid amplification in real-time. These methods generally take advantage of fluorescent labels (e.g., fluorescent dyes) that indicate the amount of nucleic acid being amplified, and utilize the relationship between the number of cycles required to achieve a chosen level of fluorescence signal and the concentration of amplifiable targets present at the initiation of the PCR process. For example, European Patent Application No. 94112728 (Publication number EP/0640828) describes a quantitative assay for an amplifiable nucleic acid target sequence which correlates the number of thermal cycles required to reach a certain concentration of target sequence to the amount of target DNA present at the beginning of the PCR process. In this assay system, a set of reaction mixtures are prepared for amplification, with one preparation including an unknown concentration of target sequence in a test sample and others containing known concentrations (standards) of the sequence. The reaction mixtures also contain a fluorescent dye that fluoresces when bound to double-stranded DNA.

[0009] The reaction mixtures are thermally cycled in separate reaction vessels for a number of cycles to achieve a sufficient amplification of the targets. The fluorescence emitted from the reaction mixtures is monitored in real-time as the amplification reactions occur, and the number of cycles necessary for each reaction mixture to fluoresce to an arbitrary cutoff level (arbitrary fluorescent value, or AFV) is determined. The AFV is chosen to be in a region of the amplification curves that is parallel among the different standards (e.g., from 0.1 to 0.5 times the maximum fluorescence value obtained by the standard using the highest initial known target nucleic acid concentration). The number of cycles necessary for each of the standards to reach the AFV is determined, and a regression line is fitted to the data that relates the initial target nucleic acid amount to the number of cycles (i.e., the threshold cycle number) needed to reach the AFV. To determine the unknown starting quantity of the target nucleic acid sequence in the sample, the number of cycles needed to reach the AFV is determined for the sample. This threshold cycle number (which can be fractional) is entered into the equation of the fitted regression line and the equation returns a value that is the initial amount of the target nucleic acid sequence in the sample.

[0010] The primary disadvantage of this method for determining an unknown starting quantity of a target nucleic acid sequence in a sample is that differences in background signal, noise, or reaction efficiency between the reaction mixtures being amplified in different reaction vessels may bias the calculation of the threshold cycle numbers. Consequently, several of the data points used to generate the regression line may deviate significantly from linearity, resulting in inaccurate quantitation of the unknown starting quantity of the target nucleic acid sequence in the sample. Small differences in the selection of threshold cycle numbers used in quantitation algorithms may have a substantial effect on the ultimate accuracy of quantitation. Thus, there remains a need to provide an objective and automatic method of selecting threshold values that will allow users of amplification methods to determine the initial concentrations of target nucleic acid sequences more accurately and reliably than present methods.

[0011] It is therefore an object of the present invention to provide improved methods and computer program products for determining a threshold value in a nucleic acid amplification reaction. The threshold value may be a threshold cycle number in a thermal cycling amplification reaction, or the threshold value may be a time value (e.g., an elapsed time of amplification) in an isothermal nucleic acid amplification reaction.

[0012] It is another object of the present invention to provide improved methods and computer program products for determining quantities of nucleic acid sequences in samples.

[0013] According to a first embodiment, the invention provides a computer program product readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring at a plurality of different times during a nucleic acid amplification reaction at least one signal whose intensity is related to a quantity of a nucleic acid sequence being amplified in the reaction. The computer program product embodies a program of instructions executable by the machine to perform the steps of deriving a growth curve from measurements of the signal; calculating a derivative of the growth curve; identifying a characteristic of the derivative; and determining a cycle number (which may be fractional) associated with the characteristic of the derivative. The step of calculating a derivative of the growth curve preferably comprises calculating second derivative values of the growth curve at a number of different cycles in the reaction to yield a plurality of second derivative data points. The characteristic of the derivative is preferably a positive peak of the second derivative, and the step of determining the cycle number associated with the positive peak preferably comprises fitting a second order curve to the second derivative data points and calculating the threshold cycle number as the location, in cycles, of a peak of the second order curve. Alternatively, the characteristic of the derivative used to determine the threshold cycle number may comprise a negative peak of the second derivative, a zero crossing of the second derivative, or a positive peak of the first derivative.

[0014] According to a second embodiment, the invention provides a computer program product for determining a threshold time value in a nucleic acid amplification reaction. The method implemented with the computer program product is particularly useful for determining a threshold time value (e.g., an elapsed time of amplification required to reach a threshold level) in an isothermal nucleic acid amplification reaction. The computer program product is readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring at a plurality of different times during a nucleic acid amplification reaction at least one signal whose intensity is related to a quantity of a nucleic acid sequence being amplified in the reaction. The computer program product embodies a program of instructions executable by the machine to perform the steps of deriving a growth curve from measurements of the signal; calculating a derivative of the growth curve; identifying a characteristic of the derivative; and determining a time value associated with the characteristic of the derivative. The step of calculating a derivative of the growth curve preferably comprises calculating second derivative values of the growth curve at a number of different times in the reaction to yield a plurality of second derivative data points. The characteristic of the derivative is preferably a positive peak of the second derivative, and the step of determining the time value associated with the positive peak preferably comprises fitting a second order curve to the second derivative data points and calculating the threshold time value as the location of a peak of the second order curve. Alternatively, the characteristic of the derivative used to determine the threshold time value may comprise a negative peak-of the second derivative, a zero crossing of the second derivative, or a positive peak of the first derivative.

[0015] Using derivatives of growth curves to determine threshold values provides for highly reproducible threshold values even when there is significant variation (e.g., in terms of timing, optics, or noise due to other sources) between the reaction sites at which the various test and calibration samples are amplified. The threshold value for each target nucleic acid sequence being amplified in a particular reaction is based solely on the data from that reaction, not from all of the reactions in a batch so that a single discrepant reaction in the batch will not bias the calculation of threshold values for target nucleic acid sequences at other reaction sites.

[0016] According to another embodiment, the invention provides a computer program product for determining a starting quantity of a nucleic acid sequence in a test sample. The computer program product is readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring signals indicative of the quantities of a target nucleic acid sequence being amplified in a test sample, containing an unknown starting quantity of the target nucleic acid sequence, and of a calibration nucleic acid sequence being amplified in a plurality of calibration samples, containing respective known starting quantities of the calibration nucleic acid sequence. The computer program product embodies a program of instructions executable by the machine to perform the step of determining a respective threshold value for the target nucleic acid sequence in the test sample and for each of the known starting quantities of the calibration nucleic acid sequence in the calibration samples. Each threshold value is determined for a nucleic acid sequence in a respective sample by deriving a growth curve for the nucleic acid sequence from the measured signals; calculating a derivative of the growth curve; identifying a characteristic of the derivative; and determining the threshold value associated with the characteristic of the derivative. The computer program product further embodies a program of instructions executable by the machine to perform the step of deriving a calibration curve from the threshold values determined for the known starting quantities of the nucleic acid sequence in the calibration samples and determining the starting quantity of the target nucleic acid sequence in the test sample using the calibration curve and the threshold value determined for the target sequence in the test sample.

[0017] According to another embodiment, the invention provides a computer program product for determining an unknown starting quantity of a target nucleic acid sequence in a test sample using quantitative internal controls. The computer program product is readable by a machine having at least one detection mechanism for measuring (1) signals indicative of the respective quantities of a target nucleic acid sequence in a test sample and of a first internal control being amplified in a first nucleic acid amplification reaction, wherein the first internal control comprises a second nucleic acid sequence different than the target nucleic acid sequence in the test sample; (2) signals indicative of the respective quantities of a first standard and of a second internal control being amplified in a second nucleic acid amplification reaction, wherein the first standard comprises a first known starting quantity of a calibration nucleic acid sequence different than the second nucleic acid sequence, and wherein the second internal control comprises the second nucleic acid sequence; and (3) signals indicative of the respective quantities of a second standard and of a third internal control being amplified in a third nucleic acid amplification reaction, wherein the second standard comprises a second known starting quantity of the calibration nucleic acid sequence, the third internal control comprises the second nucleic acid sequence, and the starting quantity of the second nucleic acid sequence is substantially the same in each of the amplification reactions. The computer program product embodies a program of instructions executable by the machine to perform the steps of (a) determining a respective threshold value for each of the standards, each of the internal controls, and the target nucleic acid sequence in the test sample; (b) normalizing the threshold value determined for the target nucleic acid sequence in the test sample to the threshold value determined for the first internal control; (c) normalizing the threshold values determined for the first and second standards to the threshold values determined for the second and third internal controls, respectively; (d) deriving a calibration curve from the known starting quantities and the normalized threshold values of the first and second standards; and (e) determining the starting quantity of the target nucleic acid sequence in the test sample using the calibration curve and the normalized threshold value determined for the target sequence in the test sample. The normalization of the threshold values to internal controls corrects for factors affecting the different reactions (e.g., the presence of inhibitors or unstable enzymes in the reaction). The threshold values are normalized for any such effects to provide greater accuracy in the calibration curve and in the quantitation of the unknown quantity of the target sequence in the test sample.

[0018] According to another embodiment, the invention provides a computer program product for determining an unknown starting quantity of a first target nucleic acid sequence in a test sample by amplifying the first nucleic acid sequence together with a plurality of standards in the same reaction vessel. The computer program product is readable by a machine having at least one detection mechanism operatively coupled thereto for detecting and measuring signals indicative of the respective quantities of a first nucleic acid sequence, a first standard, and a second standard being amplified in a reaction vessel. The first standard comprises a known starting quantity of a second nucleic acid sequence different than the first nucleic acid sequence, and the second standard comprises a known starting quantity of a third nucleic acid sequence different than the first and second nucleic acid sequences. The computer program product embodies a program of instructions executable by the machine to perform the steps of (a) determining respective threshold values for the first nucleic acid sequence, first standard, and second standard (b) deriving a calibration curve from the known starting quantities and from the threshold values determined for the first and second standards; and (c) determining the starting quantity of the first nucleic acid sequence in the test sample using the calibration curve and the threshold value determined for the first nucleic acid sequence. One advantage of this method is that a calibration curve is developed based only on the reaction in which the unknown quantity of the target nucleic acid sequence is being amplified. Consequently, the method reduces problems arising from the variability between reactions occurring in different reaction vessels. Another advantage of the method is that it reduces the number of reaction sites and the amount of expensive reagents required to perform an assay.

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] FIGS.

[0026]

[0027]

[0028] FIGS.

[0029]

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] FIGS.

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] The present invention provides methods, apparatus, and computer program products for determining quantities of target nucleic acid sequences in samples.

[0079] In more detail to FIGS.

[0080] The major walls

[0081] As shown in

[0082] The walls

[0083] Referring again to FIGS.

[0084] Referring again to FIGS.

[0085] The plunger

[0086] Referring to _{1 }_{1 }_{1}

[0087] The stroke of the plunger

[0088] Referring now to _{1 }

[0089] When the plunger _{2 }_{1 }_{1 }_{2}

[0090] It is presently preferred to pressurize the chamber to a pressure in the range of 2 to 50 psi above ambient pressure. This range is presently preferred because

[0091] Referring again to

_{1}_{1}_{2}_{2}

[0092] where:

[0093] P_{1 }

[0094] V_{1 }_{1 }

[0095] P_{2 }

[0096] V_{2 }_{2 }

[0097] To ensure the desired pressurization P_{2 }_{3 }_{1}_{2 }_{2}_{1}_{1 }_{2 }_{1 }_{1 }_{1 }_{2 }_{3 }_{2 }_{2 }

[0098] In selecting suitable dimensions for the channel _{3 }_{1}_{2}_{1}_{2 }_{2 }_{3 }_{2 }_{1 }_{1}_{2 }_{2 }

[0099] The pressure control grooves

[0100] Although the pressure control grooves _{1 }_{2 }_{1}_{2 }_{2}_{1}

[0101] Referring again to

[0102] The side walls

[0103] Optimum optical sensitivity may be attained by maximizing the optical path length of the light beams exciting the labeled analytes in the reaction mixture and the emitted light that is detected, as represented by the equation:

_{o}_{i}

[0104] where I_{0 }_{i }

[0105] The thin, flat reaction vessel

[0106] More preferably, the vessel

[0107] In the preferred embodiment, the reaction vessel

[0108] The frame

[0109] As shown in

[0110] The reaction vessel

[0111] A preferred method for fabricating the reaction vessel

[0112] The major walls

[0113] The film is then sealed to the frame

[0114] Many variations to this fabrication procedure are possible. For example, in an alternative embodiment, the film is stretched across the bottom portion of the frame

[0115] The plunger

[0116] Referring again to

[0117] Ceramic plates are presently preferred because their inside surfaces may be conveniently machined to very high smoothness for high wear resistance, high chemical resistance, and good thermal contact to the flexible walls of the reaction vessel. Ceramic plates can also be made very thin, preferably between about 0.6 and 1.3 mm, for low thermal mass to provide for extremely rapid temperature changes. A plate made from ceramic is also both a good thermal conductor and an electrical insulator, so that the temperature of the plate may be well controlled using a resistive heating element coupled to the plate.

[0118] Various thermal elements may be employed to heat and/or cool the plates

[0119] Referring to

[0120] The heating element

[0121] It is important that the plates have a low thermal mass to enable rapid heating and cooling of the plates. In particular, it is presently preferred that each of the plates has a thermal mass less than about 5 J/° C., more preferably less than 3 J/° C., and most preferably less than 1 J/° C. As used herein, the term thermal mass of a plate is defined as the specific heat of the plate multiplied by the mass of the plate. In addition, each plate should be large enough to cover a respective major wall of the reaction chamber. In the presently preferred embodiment, for example, each of the plates has a width X in the range of 2 to 22 mm, a length Y in the range of 2 to 22 mm, and a thickness in the range of 0.5 to 5 mm. The width X and length Y of each plate is selected to be slightly larger than the width and length of the reaction chamber. Moreover, each plate preferably has an angled bottom portion matching the geometry of the bottom portion of the reaction chamber, as is described below with reference to

[0122]

[0123] The heat-exchanging module

[0124] The optics assemblies

[0125] As shown in

[0126] The side walls

[0127] Referring again to

[0128] Although it is presently preferred to locate the optics assemblies

[0129] The heat-exchanging module

[0130] The housing

[0131] The opposing plates

[0132] FIGS.

[0133] The mounting plate

[0134]

[0135] Referring again to

[0136] In addition, the inner surfaces of the plates

[0137] Referring again to

[0138] Referring again to

[0139] Referring again to

[0140] Labeling of nucleic acid sequences may be achieved by a number of means, including by chemical modification of a nucleic acid primer or probe. Suitable fluorescent labels may include non-covalently binding labels (e.g., intercalating dyes) such as ethidium bromide, propidium bromide, chromomycin, acridine orange, and the like. However, in the practice of the present invention the use of covalently-binding fluorescent agents is preferred. Such covalently-binding fluorescent labels include fluorescein and derivatives thereof such as FAM, HEX, TET and JOE (all of which can be obtained from PE Biosystems, Foster City, Calif.); rhodamine and derivatives such as Texas Red (Molecular Probes, Eugene, Oreg.); ROX and TAMRA (PE Biosystems, Foster City, Calif.); Lucifer Yellow; coumarin derivatives and the like. Another preferred indicator of nucleic acid concentration is fluorescence energy-transfer (FET), in which a fluorescent reporter (or “donor”) label and a quencher (or “acceptor”) label are used in tandem to produce a detectable signal that is proportional to the amount of amplified nucleic acid product (e.g., in the form of double-stranded nucleic acid) present in the reaction mixture. Yet another detection method useful in the practice of the present invention is fluorescence polarization (FP) detection of nucleic acid amplification. Further, although fluorescence excitation and emission detection is a preferred embodiment, optical detection methods such as those used in direct absorption and/or transmission with on-axis geometries are also within the scope of the present invention. The quantity of a target nucleic acid sequence may also be measured using time decay fluorescence. Additionally, the concentration of a target nucleic acid sequence may be indicated by phosphorescent signals, chemiluminescent signals, or electrochemiluminescent signals.

[0141]

[0142] According to the present invention, multiple light sources are used to provide excitation beams to the dyes in multiple excitation wavelength ranges. Each light source provides excitation light in a wavelength range matched to the peak excitation range of a respective one of the dyes. In the preferred embodiment, the light sources are blue and green LEDs.

[0143]

[0144]

[0145] The lower housing element

[0146] The optics assembly

[0147] The optics assembly

[0148] Referring to

[0149] In this embodiment, a pair of 583 nm low pass filters

[0150] The excitation assembly

[0151] When the blue LEDs

[0152]

[0153] The lower housing element

[0154] The optics assembly

[0155] The optics assembly

[0156] Referring to

[0157] In this embodiment, the set of filters preferably includes a 515 nm Schott Glass® filter

[0158] Although it is presently preferred to position a pair of high pass filters in front of each detector for double filtering of light, a single filter may be used in alternative embodiments. In addition, a lens

[0159] Referring again to

[0160] Further, the portion of the light having a wavelength in the range of about

[0161]

[0162] The term “thermal cycling” is herein intended to mean at least one change of temperature, i.e. increase or decrease of temperature, in a reaction mixture. Therefore, samples undergoing thermal cycling may shift from one temperature to another and then stabilize at that temperature, transition to a second temperature or return to the starting temperature. The temperature cycle may be performed only once or may be repeated as many times as required to study or complete the particular chemical reaction of interest. Due to space limitations in patent drawings, the thermal cycler

[0163] Each of the reaction sites in the thermal cycler

[0164] In embodiments in which the base instrument

[0165]

[0166] The base instrument

[0167] Each heater power and source control circuit

[0168]

[0169] The module further includes four light sources, such as LEDs

[0170] The module additionally includes a signal conditioning/gain select/offset adjust block

[0171] Referring again to

[0172] In operation, the reactor system

[0173] According to a first mode of operation, the thermal cycler

[0174] The sample may be mixed with chemicals necessary for the intended reaction (e.g., PCR reagents and fluorescent probes for labeling the nucleic acid sequences to be amplified) prior to being added to the chamber

[0175] Referring again to

[0176] Referring again to

[0177] The reaction mixtures contained in the vessels

[0178] The controller may optionally be programmed to implement a modified version of PID control described in International Publication Number WO 99/48608 published Sep. 30, 1999, the disclosure of which is incorporated by reference herein. In this modified version of PID control, the controller is programmed to compensate for thermal lag between the plates

[0179] To compensate for the thermal lag during heating steps (i.e., to raise the temperature of the reaction mixture to a desired set point temperature that is higher than the previous set point temperature), the controller sets a variable target temperature that initially exceeds the desired set point temperature. For example, if the set point temperature is 95° C., the initial value of the variable target temperature may be set 2 to 10° C. higher. The controller next determines a level of power to be supplied to the heating elements to raise the temperature of the plates

[0180] When the temperature of the plates

[0181] When the average plate temperature is greater than or equal to the cutoff value, the controller decreases the variable target temperature, preferably by exponentially decaying the amount by which the variable target temperature exceeds the set point temperature. For example, the amount by which the variable target temperature exceeds the desired set point temperature may be exponentially decayed as a function of time according to the equation:

_{max}^{(−t/tau)}

[0182] where Δ is equal to the amount by which the variable target temperature exceeds the desired set point temperature, Δ_{max }

[0183] After decreasing the variable target temperature, the controller determines a new level of power to be supplied to the heating elements to raise the temperature of the plates

[0184] To compensate for the thermal lag during cooling steps (i.e., to lower the temperature of the reaction mixture to a desired set point temperature that is lower than the previous set point temperature), the controller preferably activates the fan

[0185] The controller next determines a level of power to be supplied to the heating elements to raise the temperature of the plates

[0186] Referring again to

[0187] There are four pairs of LEDs

[0188] Following the dark reading, a “light reading” is taken in each of the four primary optical detection channels as follows. The first pair of LEDs

[0189] Next, as shown in

[0190] Next, as shown in

[0191] Next, as shown in

[0192] The spectrum of the fluorescence that is emitted by the dyes used for detection is usually broad. As a result, when an individual dye (e.g., FAM, TAMRA, TET, or ROX) emits fluorescence from the reaction vessel

[0193] In the preferred embodiment, the controller is programmed to convert the output signals of the detectors to values indicating the true signal from each dye in a lo reaction mixture using linear algebra and a calibration matrix. A preferred method for developing the calibration matrix will now be described using the four-channel optical system of the preferred embodiment as an example. First, a reaction vessel containing only reaction buffer is optically read using optics assemblies

[0194] Next, a reaction mixture containing a known concentration (e.g., 100 nM) of dye #1 is placed into the vessel and again the four channels are read. The four numbers produced are called Rawdye(I,

[0195] where I indicates the detection channel, and J indicates the dye number.

[0196] The matrix Netdye(I, J) is then inverted using standard numerical methods (such as Gaussian elimination) to obtain a new matrix called the calibration matrix Cal(I,J). Note that the matrix product of Netdye(I, J)*Cal (I,J) is the unity matrix. Now, any reaction mixture can be read and the raw mixed fluorescent signals detected and measured by the four detectors may be converted to values representative of the individual signal emitted by each dye. The optical reading of the mixture produces four numbers called RawMix(I). The reaction buffer values are then subtracted from the raw mix values to obtain four numbers called Mix(I) as follows:

[0197] Next, the true dye signals are obtained by matrix multiplication as follows:

[0198] In the above equation, the factor of 100 comes from the fact that a concentration of 100 nM was used for the initial calibration measurements. The concentration of 100 nM is used for purposes of example only and is not intended to limit the scope of the invention. In general, the dye concentrations for calibration measurements should be somewhere in the range of 25 to 2,000 nM depending upon the fluorescent efficiency (strength) of the dyes and their use in a particular assay. When displayed to a user, the fluorescent signal values may be normalized to an arbitrary scale having arbitrary units of fluorescent intensity (e.g., a scale ranging from 0 to 1000 arbitrary units).

[0199] Referring again to FIGS.

[0200] As one example, calibration matrices could be stored for three different dye sets to be used with three different sizes of reaction vessels (e.g., 25 μl, 50 μl, 100 μl) for a total of nine different sets of calibration matrices. Of course, this is just one example, and many other combinations will be apparent to one skilled in the art upon reading this description. Further, in alternative embodiments, the control software may include functionality to guide the end user through the calibration procedure to enable the user to store and use calibration data for his or her own desired combination of dyes and reaction vessel size.

[0201] In one possible implementation of the four-channel system, three of the optical channels are used to detect amplified nucleic acid sequences while the fourth channel is used to monitor an internal control to check the performance of the system. For example, beta actin is often used as an internal control in nucleic acid amplification reactions because it has a predictable amplification response and can be easily labeled and monitored to verify that the amplification is occurring properly. In another possible implementation of the four-channel system, two of the optical channels are utilized to detect target nucleic acid sequences, one of the channels is used to monitor an internal control, and the fourth channel is used to monitor a passive normalizer. The passive normalizer is a dye that is placed in a reaction mixture in a known concentration and in a free form so that it will not label any target nucleic acid sequence. For example, ROX in a concentration of 100 to 500 nM makes a suitable passive normalizer. Because the passive normalizer is placed in a reaction mixture in a free form, the intensity of the fluorescent signal output by the passive normalizer is substantially unaffected by the presence or absence of a target nucleic acid sequence in the reaction mixture. The intensity of the signal does vary, however, due to such effects as evaporation of the mixture, variances in reaction vessel shapes, or air bubbles in the vessel. The intensity of the signal from the passive normalizer is monitored throughout the reaction and used to normalize the optical signals collected from the other three detection channels. If the signal from the passive normalizer changes due to evaporation, variances in reaction vessel shapes, or air bubbles in the vessel, the signals received in the other three detection channels are normalized for these variances.

[0202] Referring again to

[0203]

[0204] In particular, it is presently preferred to calculate a second derivative (with respect to cycle number) of the growth curve and to calculate the threshold cycle number as the location, in cycles, of the positive peak of the second derivative. For example,

[0205]

[0206] FIGS.

[0207] where X is equal to the cycle number, Optic(X) is equal to the signal value at cycle number X, and m and b are fitted parameters of the line. The effect of the background subtraction is to subtract the baseline signal and its linear drift from the signal values.

[0208] In step _{(X−4)}_{(X−3)}_{(X)}_{(X−2) }_{(X−2) }

_{X−2}_{X}_{X−2}_{X−4}

[0209] where k is equal to a constant multiplier (e.g., 5). The purpose of the constant multiplier is to make the second derivative curve (

[0210] The derivation of equation (1) will now be explained with reference to _{X−2}

_{X−2}_{X−1}_{X−3}

[0211] The first derivative of the growth curve at point Optic(_{X−1}

_{X−1}_{X}_{X−2}

[0212] In addition, the first derivative of the growth curve at point Optic(_{X−3}

[0213] 1stDeriv(_{X−3}_{X−2}_{X−4}

[0214] Combining equations (2), (3), and (4) and multiplying by the constant multiplier k yields equation (1).

[0215] Equation (1) may be used to calculate the second derivative of the growth curve at any point on the curve for which the two prior and two subsequent signal values are known. This is not possible, however, for the last two signal values on the growth curve. Therefore, different equations are necessary for second derivative calculations for these points.

[0216] Referring to _{(X−1) }

_{X−1}_{X−1}_{X−2}

[0217] The first derivative of the growth curve at point Optic(_{X−2}

_{X−2}_{X−1}_{X−3}

[0218] Combining equations (5) and (6) and multiplying by the constant multiplier k yields equation (7):

_{X−1}_{(}_{X−1}_{X−3}

[0219] Equation (7) may be used to calculate the second derivative of the growth curve at any point for which at least two previous and one subsequent signal values are known. If no subsequent signal value is known, then the second derivative may be calculated at a point Optic(x) using another equation which will now be described with reference to

_{X}_{X}_{(}_{X−1}_{X−1}

[0220] The first derivative of the growth curve at point Optic(_{X−1}

_{X−}_{X}_{(}_{X−2}

[0221] Combining equations (3) and (8) and multiplying by the constant multiplier k yields equation (9):

_{X}_{X}_{X−1}_{X−2}

[0222] In the preferred embodiment, the controller displays the growth curve and the second derivative of the growth curve to the user in real-time on a graphical user interface. When a new fluorescent signal value Optic(x) is received, the controller calculates a second derivative of the growth curve at Optic(x) using equation (9). When a subsequent signal value optic(_{X+1}_{X+2}

[0223] In step

[0224] Referring again to

[0225]

[0226] FIGS.

[0227] Referring again to

[0228] FIGS.

[0229] FIGS.

[0230] Preferred methods for calculating the first derivative data points will now be described with reference to _{(X−4)}_{(X−3)}_{(X)}_{(X−2) }_{(X−1) }

_{X−1}_{X}_{X−2)]/}

[0231] Equation (3) may be used to calculate the first derivative of the growth curve at any point on the curve for which at least one prior and one subsequent signal value is known. This is not possible, however, for the last signal value on the growth curve. Therefore, a different equation is necessary to calculate a first derivative value at the last point. Still referring to

_{X}_{X}_{X−1}

[0232] The controller preferably displays the growth curve and the first derivative of the growth curve to the user in real-time on a graphical user interface. When a new fluorescent signal value Optic(x) is received, the controller calculates a first derivative of the growth curve at Optic(x) using equation (10). When a subsequent signal value Optic(x+

[0233] In step

[0234] Referring again to

[0235] Referring again to

[0236] The following three examples of operation demonstrate various different methods for using threshold cycle values to determine the unknown starting quantity of a target nucleic acid sequence in a test sample according to the present invention.

[0237] Referring to

[0238]

[0239]

[0240] To determine the unknown starting quantity of each of the three target nucleic acid sequences in a test sample, a respective threshold value is determined for each target sequence. The threshold value is then entered into the equation of the corresponding calibration curve and the equation returns a value that is the starting quantity of the target nucleic acid sequence in the test sample. For example,

[0241] This example is similar to example 1, except that in example 2 each threshold value determined for a nucleic acid sequence is normalized by the threshold value determined for a quantitative internal control. Referring to

[0242]

[0243]

[0244] Referring to

[0245] In this example, the calibration nucleic acid sequences (standards) are amplified together in the same reaction vessel with the unknown quantity of a target nucleic acid sequence in a test sample. Referring to

[0246]

[0247]

[0248] One advantage to using internal standards is that a calibration curve is developed based only on the reaction in which the unknown quantity of the target nucleic acid sequence is being amplified. Consequently, the method reduces problems arising from the variability between reactions occurring in different reaction vessels. Another advantage of the method is that it reduces the number of reaction sites and the amount of expensive reagents required to perform an assay.

[0249] Although the above description contains many specificities, it is to be understood that many different modifications or substitutions may be made to the methods, apparatus, and computer program products described without departing from the broad scope of the invention. For example, the means for amplifying the test and calibration samples need not be the specialized thermal cycler described herein. The means for amplifying the test and calibration samples may comprise a metal block having a plurality of wells for receiving the samples. Alternatively, the means for amplifying the test and calibration samples may comprise a forced air system for heating and cooling samples contained in capillary tubes. These and other apparatuses for amplifying and detecting nucleic acid are known in the art.

[0250] Moreover, the controller for controlling the operation of the apparatus may be a personal or network computer linked to the heat-exchanger or may comprise a microprocessor and memory built into the heat-exchanging instrument. The computer program product (e.g., software) readable by the controller may comprise a storage medium (e.g., a disk) embodying the program instructions. Alternatively, the computer program product may be an electronic file stored in the memory of the controller or downloadable to the controller. Further, the specialized reaction vessels described above are preferred, but the apparatus and methods of the present invention are applicable to any type of vessel including plastic reaction tubes, glass capillary tubes, microtiter plates, cartridges or cuvettes, etc.

[0251] In addition, the threshold value (e.g., cycle number or time value) determined using the methods of the present invention has other uses besides quantitation of an unknown quantity of a nucleic acid sequence. For example, the threshold value may be used to determine an optimal termination point for a nucleic acid amplification reaction so that the reaction may be terminated prior to reaching the plateau phase to prevent degradation of amplicons and/or accumulation of undesired products (e.g., primer dimers).

[0252] Further, the mathematical methods described above for calculating derivatives and threshold criteria are examples only and other methods may be used to obtain similar data. For example, one could fit a mathematical function as an approximation to an entire growth curve and then calculate derivatives based on that function. Moreover, the terminology in the claims related to the steps of deriving growth curves, calculating derivatives, deriving calibration curves, and/or fitting curves to data points is intended to include the processing of data (e.g., x-y data) and variables internal to a processing unit (e.g., a computer) containing memory and is not limited to the physical acts of printing, plotting, or displaying lines, curves, or graphs.

[0253] Therefore, the scope of the invention should be determined by the following claims and their legal equivalents.