Systems and methods for determining cross-talk coefficients in PCR and other data sets
Systems and methods for determining cross-talk coefficients in curves, such as sigmoid-type or growth curves, and PCR curves and nucleic acid melting curves in particular, as well as for applying the cross-talk coefficients to produce cross-talk corrected data sets using a linear subtractive model. Cross-talk signal coefficients are determined using cross-talk data acquired across the entire signal acquisition range. Analyzing across all of the signal curve data provides for a more robust cross-talk correction across the entire data acquisition range. A linear subtractive model is used to correct data sets having cross-talk components.
1. A method of determining cross-talk coefficients for a Polymerase Chain Reaction (PCR) optical detection system having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, the method comprising the steps, implemented in a processor, of:
receiving, for each optical element, a PCR data set acquired over a data acquisition range of a PCR growth process, wherein the data acquisition range represents a plurality of PCR cycles, and wherein each PCR data set includes a data value for each PCR cycle in the acquisition range;
receiving, for each other optical element, a cross-talk data set acquired over the acquisition range simultaneously with the PCR data set, and wherein each cross-talk data set includes a data value for each PCR cycle in the acquisition range; and
determining cross-talk coefficients using the PCR and cross-talk data sets over the acquisition range, wherein determining includes, for each optical element, minimizing a sum of the squares between each PCR data set and cross-talk data set over the acquisition range using an equation of the form:
min
[
∑
i
(
XTSignal
i
-
q
*
Signal
i
)
2
]
,
wherein i is a PCR cycle number, wherein Signal i is the PCR data value for cycle i for each optical element, wherein XTSignal i is the cross-talk data value for cycle i for each other optical element, and wherein q is a multiplicative gain factor.
2. The method of claim 1 , wherein the acquisition range includes a baseline region, a growth region and a plateau region.
3. The method of claim 1 , wherein the data acquisition range represents a plurality of PCR cycles, and wherein determining cross-talk coefficients includes minimizing a sum of the absolute values between each PCR data set and cross-talk data set over the acquisition range.
4. A method of determining cross-talk coefficients for a Polymerase Chain Reaction (PCR) optical detection system having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, the method comprising the steps, implemented in a processor, of:
receiving, for each optical element, a PCR data set acquired over a data acquisition range of a PCR growth process, wherein the data acquisition range represents a plurality of PCR cycles, and wherein each PCR data set includes a data value for each PCR cycle in the acquisition range;
receiving, for each other optical element, a cross-talk data set acquired over the acquisition range simultaneously with the PCR data set, and wherein each cross-talk data set includes a data value for each PCR cycle in the acquisition range; and
determining cross-talk coefficients using the PCR and cross-talk data sets over the acquisition range, wherein determining includes, for each optical element, minimizing a sum of the squares between each PCR data set and cross-talk data set over the acquisition range using an equation of the form:
min
[
∑
i
[
(
XTSignal
1
i
-
(
r
+
s
*
i
+
q
1
*
Signal
i
)
)
2
+
(
XTSignal
2
i
-
(
r
+
s
*
i
+
q
2
*
Signal
i
)
)
2
+
(
XTSignal
3
i
-
(
r
+
s
*
i
+
q
3
*
Signal
i
)
)
2
]
]
wherein i is a PCR cycle number, wherein Signal i is the PCR data value for cycle for each optical element, wherein XTSignal i is the cross-talk data value for cycle i for each other optical element, wherein r is a common offset, wherein s is a common slope and wherein q 1 , q 2 and q 3 are multiplicative gain factors.
5. A method of determining cross-talk coefficients for a Polymerase Chain Reaction (PCR) optical detection system having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, the method comprising the steps, implemented in a processor, of:
receiving, for each optical element, a PCR data set acquired over a data acquisition range of a PCR growth process, wherein the data acquisition range represents a plurality of PCR cycles, and wherein each PCR data set includes a data value for each PCR cycle in the acquisition range;
receiving, for each other optical element, a cross-talk data set acquired over the acquisition range simultaneously with the PCR data set, and wherein each cross-talk data set includes a data value for each PCR cycle in the acquisition range; and
determining cross-talk coefficients using the PCR and cross-talk data sets over the acquisition range, wherein determining includes, for each optical element, minimizing a sum of the squares between each PCR data set and cross-talk data set over the acquisition range using an equation of the form:
min
[
∑
i
(
XTSignal
i
-
(
r
+
s
*
i
+
q
*
Signal
i
)
)
2
]
,
wherein i is a PCR cycle number, wherein Signal i is the PCR data value for cycle i for each optical element, wherein XTSignal i is the cross-talk data value for cycle i for each other optical element, wherein r is an offset, wherein s is a slope and wherein q is a multiplicative gain factor.
6. The method of claim 1 , further including:
determining a baseline for each PCR data set and each cross-talk data set; and
prior to determining cross-talk coefficients, subtracting the respective baseline from each data set.
7. The method of claim 6 , wherein determining a baseline includes performing a linear regression on a data set between defined baseline start and baseline stop positions.
8. The method of claim 6 , wherein determining a baseline includes curve fitting a double sigmoid function to identify slope and intercept values.
9. The method of claim 1 , further including removing outlier points from one or more of the PCR data sets and cross-talk data sets prior to determining cross-talk coefficients.
10. The method of claim 1 , wherein the optical elements include one or more filters, each filter allowing light of a different specific wavelength range to pass.
11. The method of claim 10 , wherein the optical elements include at least four filters.
12. The method of claim 1 , further including:
applying the determined cross-talk coefficients to a PCR data set using a linear subtractive model to produce a cross-talk corrected data set.
13. The method of claim 12 , wherein the linear subtractive model includes an equation of the form:
f
iC
=
f
i
-
(
∑
j
≠
i
a
ij
f
j
)
where f i is the measured signal in channel (i) and f iC is the cross-talk corrected signal in channel (i), and where the coefficients a ij denote the cross-talk coefficients from channel (j) to channel (i).
14. The method of claim 12 , wherein the linear subtractive model includes an equation of the form:
f
iC
=
f
i
-
(
∑
j
≠
i
a
ij
f
j
)
-
(
r
+
s
*
i
)
where f i is the measured signal in channel (i) and f iC is the cross-talk corrected signal in channel (i), where the coefficients a ij denote the cross talk coefficients from channel (j) to channel (i), and where r and s are a gain and a linear term, respectively, that are common for all channels (i).
15. The method of claim 12 , wherein the linear subtractive model includes an equation of the form:
f
iC
=
f
i
-
(
∑
j
≠
i
a
ij
f
j
)
-
(
r
i
+
s
i
*
i
)
where f i is the measured signal in channel (i) and f iC is the cross-talk corrected signal in channel (i), where the coefficients a ij denote the cross talk coefficients from channel (j) to channel (i), and where r i and s i are a gain and a linear term, respectively, that are different for each channel (i).
16. The method of claim 1 , further including displaying or outputting the determined crosstalk coefficients.
17. The method of claim 1 , further including storing the determined cross-talk coefficients to a memory module for later use in producing cross-talk corrected data sets.
18. A tangible computer readable medium that stores code for controlling a processor to determine cross-talk coefficients for a Polymerase Chain Reaction (PCR) optical detection system having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, the code including instructions to:
receive, for each optical element, a PCR data set acquired over a data acquisition range of a PCR growth process, the acquisition range including a baseline region, a growth region and a plateau region, wherein the data acquisition range represents a plurality of PCR cycles, and wherein each PCR data set includes a data value for each PCR cycle in the acquisition range;
receive, for each other optical element, a cross-talk data set for each filter acquired over the acquisition range simultaneously with the PCR data set, wherein each cross-talk data set includes a data value for each PCR cycle in the acquisition range; and
determine cross-talk coefficients using the PCR and cross-talk data sets over the acquisition range, wherein the instructions to determine include instructions to minimize, for each optical element, a sum of the squares between each PCR data set and cross-talk data set over the acquisition range using an equation of the form:
min
[
∑
i
(
XTSignal
i
-
q
*
Signal
i
)
2
]
,
wherein i is a PCR cycle number, wherein Signal i is the PCR data value for cycle i for each optical element, wherein XTSignal i is the cross-talk data value for cycle i for each other optical element, and wherein q is a multiplicative gain factor.
19. A kinetic Polymerase Chain Reaction (PCR) system, comprising:
an optical detection module having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, wherein said optical detection module is adapted to:
acquire, for each optical element, a PCR data set over a data acquisition range of a PCR growth process, the acquisition range including a baseline region, a growth region and a plateau region, wherein the data acquisition range represents a plurality of PCR cycles, and wherein each PCR data set includes a data value for each PCR cycle in the acquisition range; and
simultaneously acquire, for each other optical element, a cross-talk data set over the acquisition range, wherein each cross-talk data set includes a data value for each PCR cycle in the acquisition range; and
an intelligence module adapted to process the acquired PCR data sets and cross-talk data sets to determine cross-talk coefficients using the PCR and cross-talk data sets over the acquisition range by minimizing, for each optical element, a sum of the squares between each PCR data set and cross-talk data set over the acquisition range using an equation of the form:
min
[
∑
i
(
XTSignal
i
-
q
*
Signal
i
)
2
]
,
wherein i is a PCR cycle number, wherein Signal i is the PCR data value for cycle i for each optical element, wherein XTSignal i is the cross-talk data value for cycle i for each other optical element, and wherein q is a multiplicative gain factor.
20. A nucleic acid melting analysis system, comprising:
an optical detection module having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, wherein said optical detection module is adapted to:
acquire, for each optical element, a melting data set over a temperature acquisition range, and simultaneously acquire, for each other optical element, a cross-talk data set over the temperature acquisition range, wherein each melting data set includes a data value for each temperature in the temperature acquisition range, and wherein each cross-talk data set includes a data value for each temperature in the temperature acquisition range; and
determine cross-talk coefficients by minimizing, for each element, a sum of squares between each melting data set and cross-talk data set over the acquisition range by minimizing a sum of the squares between each melting data set and cross-talk data set over the temperature acquisition range using an equation of the form:
min
[
∑
i
(
XTSignal
i
-
q
*
Signal
i
)
2
]
,
wherein i is a temperature index, wherein Signal i is the melting data value for temperature index i for each optical element, wherein XTSignal i is the cross-talk data value for temperature index i for each other optical element, and wherein q is a multiplicative gain factor.
21. A method of determining cross-talk coefficients for an optical detection system having at least two optical elements, each optical element operable to isolate a different specific electromagnetic wavelength range, the method comprising the steps, implemented in a processor, of:
receiving, for each optical element, a first data set acquired over a data acquisition range of a growth process, wherein the data acquisition range represents a plurality of cycles, wherein each first data set includes a data value for each cycle in the acquisition range;
receiving, for each other optical element, a cross-talk data set acquired over the acquisition range simultaneously with the first data set, and wherein each cross-talk data set includes a data value for each cycle in the acquisition range; and
determining cross-talk coefficients using the first and cross-talk data sets over the acquisition range by minimizing, for each optical element, a sum of the squares between each first data set and cross-talk data set over the acquisition range using an equation of the form:
min
[
∑
i
(
XTSignal
i
-
q
*
Signal
i
)
2
]
,
wherein i is a cycle number, wherein Signal i is the data value of the first data set for cycle i for each optical element, wherein XTSignal i is the cross-talk data value for cycle i for each other optical element, and wherein q is a multiplicative gain factor.