Methods and systems for volume variation modeling in digital PCR
A method for performing digital polymerase chain reaction (dPCR) is provided. The method includes partitioning a biological sample volume including a plurality of target nucleic acids into a plurality of partitions, where at least one partition includes at least one target nucleic acid. The method further includes determining a model for volume variation of the plurality of partitions and determining a number of partitions including at least one target nucleic acid. The method includes generating a concentration of target nucleic acids in the biological sample based on the model for volume variation and the fraction of partitions including at least one target nucleic acid.
1. A method for performing digital polymerase chain reaction (dPCR) in a dPCR biological analysis system including a thermal cycler, a processor, a detector, and a display, the method comprising:
partitioning a biological sample volume including a plurality of target nucleic acids into a plurality of partitions, wherein at least one partition includes at least one target nucleic acid;
amplifying, with the thermal cycler, the target nucleic acids in the plurality of partitions;
generating, by the processor, a model for volume variation of the plurality of partitions based on a normal distribution of effective load volumes of the biological sample volume in the plurality of partitions;
detecting, by the detector, the amplified target nucleic acids to determine a number of partitions including at least one target nucleic acid;
calculating, by the processor, a concentration of target nucleic acids in the biological sample based on the model for volume variation and the number of partitions including at least one target nucleic acid; and
displaying, on the display, the concentration of target nucleic acids in the biological sample.
2. The method of claim 1 , wherein the concentration of target nucleic acids in the biological sample is determined by using the equation:
C
=
v
0
-
v
0
2
+
2
σ
2
ln
P
(
neg
)
σ
2
.
3. The method of claim 1 , wherein the concentration of target nucleic acids in the biological sample is determined by using the equation:
P
(
neg
)
=
erfc
[
-
1
2
(
v
0
σ
-
C
σ
)
]
erfc
[
-
1
2
(
v
0
σ
)
]
e
-
Cv
0
+
1
2
σ
2
C
2
.
4. The method of claim 1 , further comprising:
amplifying the target nucleic acids to determine the number of partitions including at least one target nucleic acid.
5. The method of claim 1 , wherein the model for volume variation is:
P
(
neg
)
=
erfc
[
-
1
2
(
v
0
σ
-
C
σ
)
]
erfc
[
-
1
2
(
v
0
σ
)
]
e
-
Cv
0
+
1
2
σ
2
C
2
.
6. The method of claim 1 , wherein the model for volume variation is:
P (neg)=exp(1/2σ 2 C 2 −C v 0 ).
7. The method of claim 1 , wherein the plurality of partitions is a plurality of reaction sites.
8. The method of claim 1 , wherein the plurality of partitions is a plurality of throughholes.
9. The method of claim 1 , wherein the plurality of partitions is a plurality of droplets.
10. A system for performing digital polymerase chain reaction (dPCR), the system comprising:
a device configured to partition a biological sample volume including a plurality of target nucleic acids into a plurality of partitions, wherein at least one partition includes at least one target nucleic acid;
a thermal cycler to amplify the plurality of target nucleic acids;
a detector for detecting the number of partitions including at least one target nucleic acid;
a memory; and
a processor configured to:
generate a concentration of target nucleic acids in the biological sample based on a model for volume variation and the number of partitions including at least one target nucleic acid, wherein the model is based on a normal distribution of effective load volume of each of the biological sample volume in the plurality of partitions; and
a display to display the concentration of target nucleic acids in the biological sample.
11. The system of claim 10 , wherein the concentration of target nucleic acids in the biological sample is determined by using the equation:
C
=
v
0
-
v
0
2
+
2
σ
2
ln
P
(
neg
)
σ
2
.
12. The system of claim 10 , wherein the concentration of target nucleic acids in the biological sample is determined by using the equation:
P
(
neg
)
=
erfc
[
-
1
2
(
v
0
σ
-
C
σ
)
]
erfc
[
-
1
2
(
v
0
σ
)
]
e
-
Cv
0
+
1
2
σ
2
C
2
.
13. The system of claim 10 , further comprising:
an amplification apparatus configured to amplify the target nucleic acids to determine the number of partitions including at least one target nucleic acid.
14. The system of claim 10 , wherein the model for volume variation is:
P
(
neg
)
=
erfc
[
-
1
2
(
v
0
σ
-
C
σ
)
]
erfc
[
-
1
2
(
v
0
σ
)
]
e
-
Cv
0
+
1
2
σ
2
C
2
.
15. The system of claim 10 , wherein the model for volume variation is:
P (neg)=exp(1/2σ 2 C 2 −C v 0 ).
16. The system of claim 10 , wherein the plurality of partitions is a plurality of reaction sites.
17. The system of claim 10 , wherein the plurality of partitions is a plurality of throughholes.
18. The system of claim 10 , wherein the plurality of partitions is a plurality of droplets.