U.S. patent application number 15/301949 was filed with the patent office on 2017-06-22 for methods and systems for pcr quantitation.
The applicant listed for this patent is LIFE TECHNOLOGIES CORPORATION. Invention is credited to David Keys, Yalei Wu.
Application Number | 20170177791 15/301949 |
Document ID | / |
Family ID | 52829492 |
Filed Date | 2017-06-22 |
United States Patent
Application |
20170177791 |
Kind Code |
A1 |
Wu; Yalei ; et al. |
June 22, 2017 |
Methods and Systems for PCR Quantitation
Abstract
A method for quantifying nucleic acid is provided. The method
includes determining a first reference threshold cycle for a first
predetermined input quantity for a reference nucleic acid,
determining a first target threshold cycle for the first
predetermined input quantity for a target nucleic acid, determining
a second reference threshold cycle for a second predetermined input
quantity for the reference nucleic acid, and determining a second
target threshold cycle, by the processor, for the second
predetermined input quantity for the target nucleic acid. The
method further includes receiving a sample threshold cycle,
determining a sample input quantity based on the first and second
reference threshold cycle and the first and second target threshold
cycle, and displaying the sample input quantity to a user.
Inventors: |
Wu; Yalei; (Foster City,
CA) ; Keys; David; (Alameda, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LIFE TECHNOLOGIES CORPORATION |
Carlsbad |
CA |
US |
|
|
Family ID: |
52829492 |
Appl. No.: |
15/301949 |
Filed: |
April 3, 2015 |
PCT Filed: |
April 3, 2015 |
PCT NO: |
PCT/US15/24249 |
371 Date: |
October 4, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61975614 |
Apr 4, 2014 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
C12Q 1/6851 20130101;
C12Q 2537/16 20130101; G16B 45/00 20190201; G16B 25/00 20190201;
C12Q 1/686 20130101; G16B 5/00 20190201; C12Q 2545/114 20130101;
G16B 30/00 20190201; G16B 40/00 20190201; C12Q 2537/16 20130101;
C12Q 1/6851 20130101; C12Q 2545/114 20130101 |
International
Class: |
G06F 19/24 20060101
G06F019/24; G06F 19/22 20060101 G06F019/22; G06F 19/26 20060101
G06F019/26; G06F 19/12 20060101 G06F019/12 |
Claims
1. A method for quantifying a nucleic acid, the method comprising:
determining a first reference threshold cycle for a first
predetermined input quantity for a reference nucleic acid;
determining a first target threshold cycle for the first
predetermined input quantity for a target nucleic acid; determining
a second reference threshold cycle for a second predetermined input
quantity for the reference nucleic acid; determining a second
target threshold cycle for the second predetermined input quantity
for the target nucleic acid; receiving a sample threshold cycle;
determining a sample input quantity based on the first and second
reference threshold cycle and the first and second target threshold
cycle; and displaying the sample input quantity to a user.
2. The method of claim 1, wherein the first and second target
thresholds are determined from a mutant detection assay.
3. The method of claim 2, wherein the first and second reference
thresholds are determined by a gene reference assay.
4. The method of claim 1, wherein the sample input quantity is
calculated with the following equation: sample input quantity
%=2.sup.-(Ct.sup.mu.sup.-Ct.sup.rf.sup.)
5. The method of claim 3, wherein the sensitivities of the mutation
detection assay and the gene reference assay are different.
6. The method of claim 3, wherein the efficiencies of the mutation
detection assay and the gene reference assay are different.
7. A system for quantifying a nucleic acid, the system comprising:
a threshold cycle determination processor configured to: determine
a first reference threshold cycle for a first predetermined input
quantity for a reference nucleic acid, determine a first target
threshold cycle for the first predetermined input quantity for a
target nucleic acid, determine a second reference threshold cycle
for a second predetermined input quantity for the reference nucleic
acid, and determine a second target threshold cycle for the second
predetermined input quantity for the target nucleic acid; a
quantity determination processor configured to: receive a sample
threshold cycle, determine the sample input quantity based on the
first and second reference threshold cycle and the first and second
target threshold cycle; and a display screen configured to display
the sample input quantity to a user.
8. The system of claim 7, wherein the first and second target
thresholds are determined from a mutant detection assay.
9. The system of claim 8, wherein the first and second reference
thresholds are determined by a gene reference assay.
10. The system of claim 7, wherein the sample input quantity is
calculated with the following equation: sample input quantity
%=2.sup.-(Ct.sup.mu.sup.-Ct.sup.rf.sup.)
11. The system of claim 9, wherein the sensitivities of the
mutation detection assay and the gene reference assay are
different.
12. The system of claim 9, wherein the efficiencies of the mutation
detection assay and the gene reference assay are different.
13. A method for quantifying a nucleic acid, the method comprising:
receiving, by a processor, at least three determined threshold
cycles for a sample, wherein each of the at least three determined
threshold cycles corresponds with a known input quantity;
generating, by the processor, a plot of threshold cycles versus
input quantity including each of the at least three determined
threshold cycles and corresponding known input quantity;
determining, by the processor, a weight measure of one of the at
least three determined threshold cycles based on two of the at
least three determined threshold cycles; determining, by the
processor, a best-fit line through the at least three determined
threshold cycles based on the weight measure; receiving, by the
processor, a plurality of fluorescence measurements from a test
sample of an unknown input quantity; determining, by the processor,
a threshold cycle of the test sample; determining, by the
processor, an input quantity of the test sample based on the
best-fit line; and displaying, on a display screen, the input
quantity to a user.
14. The method of claim 13, wherein the first and second target
thresholds are determined from a mutant detection assay.
15. The method of claim 14, wherein the first and second reference
thresholds are determined by a gene reference assay.
Description
BACKGROUND
[0001] Quantitative nucleic acid analysis is extensively used in
biological research and clinical analysis. Some of the applications
which make use of this technology include: measurement of gene
expression, monitoring of biological responses to stimuli,
genomic-level gene quantitation, and pathogen detection. Typically,
these methodologies utilize Polymerase Chain Reaction (PCR) as a
means for selectively amplifying nucleic acid sequences in a manner
that allows for their detection. While it is generally desirable to
automate the quantitation process, conventional methodologies often
require a degree of user input in the form of subjective
interpretation and/or approximation. As a result, these techniques
may suffer from reduced accuracy and significant user-induced
variability. Furthermore, in high-throughput applications where
many samples are to be processed simultaneously, it is desirable to
provide increased automation capabilities to improve the speed with
which the analysis may be conducted. The aforementioned limitations
of conventional techniques illustrate the need for an improved
method for analyzing data generated by PCR-based quantitation
techniques that may increase the potential for automation while
improving the quantitative accuracy and reproducibility of the
analysis.
SUMMARY
[0002] In one exemplary embodiment, a method for quantifying
nucleic acid is provided. The method includes determining a first
reference threshold cycle for a first predetermined input quantity
for a reference nucleic acid, determining a first target threshold
cycle for the first predetermined input quantity for a target
nucleic acid, determining a second reference threshold cycle for a
second predetermined input quantity for the reference nucleic acid,
and determining a second target threshold cycle, by the processor,
for the second predetermined input quantity for the target nucleic
acid. The method further includes receiving a sample threshold
cycle, determining a sample input quantity based on the first and
second reference threshold cycle and the first and second target
threshold cycle, and displaying the sample input quantity to a
user.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] FIG. 1 illustrates an exemplary block diagram of a computing
system for implementing the quantitation method according to
various embodiments described herein.
[0004] FIG. 2A illustrates an example of a mutant allele assay
according to various embodiments described herein.
[0005] FIG. 2B illustrates an example of a gene reference assay
according to various embodiments described herein.
[0006] FIG. 3A illustrates a plot of Ct versus input quantity
according to various embodiments described herein.
[0007] FIG. 3B illustrates a plot of Ct versus input quantity
according to various embodiments described herein.
[0008] FIG. 4 illustrates another plot of Ct versus input quantity
according to various embodiments described herein.
[0009] FIG. 5 illustrates Ct versus relative quantity according to
various embodiments described herein.
[0010] FIG. 6 illustrates a quantitation curve according various
embodiments described herein.
[0011] FIG. 7 illustrates data to support the performance of the
quantitation method according to various embodiments described
herein.
[0012] FIG. 8A and FIG. 8B illustrate several assays of the Von
Hippel-Lindau tumor suppressor, an E3 ubiquitin protein ligase
according to various embodiments described herein.
[0013] FIG. 9A and FIG. 9B illustrate the deviation of expected
mutant percentage compared with the expected mutant percentage
according to various embodiments described herein.
DETAILED DESCRIPTION
[0014] To provide a more thorough understanding of the present
invention, the following description sets forth numerous specific
details, such as specific configurations, parameters, examples, and
the like. It should be recognized, however, that such description
is not intended as a limitation on the scope of the present
invention, but is intended to provide a better description of the
exemplary embodiments.
[0015] Various embodiments described herein generally relate to
nucleic acid analysis, and more particularly, to a system and
methods for evaluating results obtained from quantitative
amplification reactions.
[0016] Those skilled in the art will recognize that the operations
of the various embodiments may be implemented using hardware,
software, firmware, or combinations thereof, as appropriate. For
example, some processes can be carried out using processors or
other digital circuitry under the control of software, firmware, or
hard-wired logic. (The term "logic" herein refers to fixed
hardware, programmable logic and/or an appropriate combination
thereof, as would be recognized by one skilled in the art to carry
out the recited functions.) Software and firmware can be stored on
computer-readable media. Some other processes can be implemented
using analog circuitry, as is well known to one of ordinary skill
in the art. Additionally, memory or other storage, as well as
communication components, may be employed in embodiments of the
invention.
[0017] FIG. 1 is a block diagram that illustrates a computer system
100 that may be employed to carry out processing functionality,
according to various embodiments, upon which embodiments of a
thermal cycler system (not shown) may utilize. Computing system 100
can include one or more processors, such as a processor 104.
Processor 104 can be implemented using a general or special purpose
processing engine such as, for example, a microprocessor,
controller or other control logic. In this example, processor 104
is connected to a bus 102 or other communication medium.
[0018] Further, it should be appreciated that a computing system
100 of FIG. 1 may be embodied in any of a number of forms, such as
a rack-mounted computer, mainframe, supercomputer, server, client,
a desktop computer, a laptop computer, a tablet computer, hand-held
computing device (e.g., PDA, cell phone, smart phone, palmtop,
etc.), cluster grid, netbook, embedded systems, or any other type
of special or general purpose computing device as may be desirable
or appropriate for a given application or environment.
Additionally, a computing system 100 can include a conventional
network system including a client/server environment and one or
more database servers, or integration with LIS/LIMS infrastructure.
A number of conventional network systems, including a local area
network (LAN) or a wide area network (WAN), and including wireless
and/or wired components, are known in the art. Additionally,
client/server environments, database servers, and networks are well
documented in the art.
[0019] Computing system 100 may include bus 102 or other
communication mechanism for communicating information, and
processor 104 coupled with bus 102 for processing information.
[0020] Computing system 100 also includes a memory 106, which can
be a random access memory (RAM) or other dynamic memory, coupled to
bus 102 for storing instructions to be executed by processor 104.
Memory 106 also may be used for storing temporary variables or
other intermediate information during execution of instructions to
be executed by processor 104. Computing system 100 further includes
a read only memory (ROM) 108 or other static storage device coupled
to bus 102 for storing static information and instructions for
processor 104.
[0021] Computing system 100 may also include a storage device 110,
such as a magnetic disk, optical disk, or solid state drive (SSD)
is provided and coupled to bus 102 for storing information and
instructions. Storage device 110 may include a media drive and a
removable storage interface. A media drive may include a drive or
other mechanism to support fixed or removable storage media, such
as a hard disk drive, a floppy disk drive, a magnetic tape drive,
an optical disk drive, a CD or DVD drive (R or RW), flash drive, or
other removable or fixed media drive. As these examples illustrate,
the storage media may include a computer-readable storage medium
having stored therein particular computer software, instructions,
or data.
[0022] In alternative embodiments, storage device 110 may include
other similar instrumentalities for allowing computer programs or
other instructions or data to be loaded into computing system 100.
Such instrumentalities may include, for example, a removable
storage unit and an interface, such as a program cartridge and
cartridge interface, a removable memory (for example, a flash
memory or other removable memory module) and memory slot, and other
removable storage units and interfaces that allow software and data
to be transferred from the storage device 110 to computing system
100.
[0023] Computing system 100 can also include a communications
interface 118. Communications interface 118 can be used to allow
software and data to be transferred between computing system 100
and external devices. Examples of communications interface 118 can
include a modem, a network interface (such as an Ethernet or other
NIC card), a communications port (such as for example, a USB port,
a RS-232C serial port), a PCMCIA slot and card, Bluetooth, etc.
Software and data transferred via communications interface 118 are
in the form of signals which can be electronic, electromagnetic,
optical or other signals capable of being received by
communications interface 118. These signals may be transmitted and
received by communications interface 118 via a channel such as a
wireless medium, wire or cable, fiber optics, or other
communications medium. Some examples of a channel include a phone
line, a cellular phone link, an RF link, a network interface, a
local or wide area network, and other communications channels.
[0024] Computing system 100 may be coupled via bus 102 to a display
112, such as a cathode ray tube (CRT) or liquid crystal display
(LCD), for displaying information to a computer user. An input
device 114, including alphanumeric and other keys, is coupled to
bus 102 for communicating information and command selections to
processor 104, for example. An input device may also be a display,
such as an LCD display, configured with touchscreen input
capabilities. Another type of user input device is cursor control
116, such as a mouse, a trackball or cursor direction keys for
communicating direction information and command selections to
processor 104 and for controlling cursor movement on display 112.
This input device typically has two degrees of freedom in two axes,
a first axis (e.g., x) and a second axis (e.g., y), that allows the
device to specify positions in a plane. A computing system 100
provides data processing and provides a level of confidence for
such data. Consistent with certain implementations of embodiments
of the present teachings, data processing and confidence values are
provided by computing system 100 in response to processor 104
executing one or more sequences of one or more instructions
contained in memory 106. Such instructions may be read into memory
106 from another computer-readable medium, such as storage device
110. Execution of the sequences of instructions contained in memory
106 causes processor 104 to perform the process states described
herein. Alternatively hard-wired circuitry may be used in place of
or in combination with software instructions to implement
embodiments of the present teachings. Thus implementations of
embodiments of the present teachings are not limited to any
specific combination of hardware circuitry and software.
[0025] The term "computer-readable medium" and "computer program
product" as used herein generally refers to any media that is
involved in providing one or more sequences or one or more
instructions to processor 104 for execution. Such instructions,
generally referred to as "computer program code" (which may be
grouped in the form of computer programs or other groupings), when
executed, enable the computing system 100 to perform features or
functions of embodiments of the present invention. These and other
forms of computer-readable media may take many forms, including but
not limited to, non-volatile media, volatile media, and
transmission media. Non-volatile media includes, for example, solid
state, optical or magnetic disks, such as storage device 110.
Volatile media includes dynamic memory, such as memory 106.
Transmission media includes coaxial cables, copper wire, and fiber
optics, including the wires that comprise bus 102.
[0026] Common forms of computer-readable media include, for
example, a floppy disk, a flexible disk, hard disk, magnetic tape,
or any other magnetic medium, a CD-ROM, any other optical medium,
punch cards, paper tape, any other physical medium with patterns of
holes, a RAM, PROM, and EPROM, a FLASH-EPROM, any other memory chip
or cartridge, a carrier wave as described hereinafter, or any other
medium from which a computer can read.
[0027] Various forms of computer readable media may be involved in
carrying one or more sequences of one or more instructions to
processor 104 for execution. For example, the instructions may
initially be carried on magnetic disk of a remote computer. The
remote computer can load the instructions into its dynamic memory
and send the instructions over a telephone line using a modem. A
modem local to computing system 100 can receive the data on the
telephone line and use an infra-red transmitter to convert the data
to an infra-red signal. An infra-red detector coupled to bus 102
can receive the data carried in the infra-red signal and place the
data on bus 102. Bus 102 carries the data to memory 106, from which
processor 104 retrieves and executes the instructions. The
instructions received by memory 106 may optionally be stored on
storage device 110 either before or after execution by processor
104.
[0028] It will be appreciated that, for clarity purposes, the above
description has described embodiments of the invention with
reference to different functional units and processors. However, it
will be apparent that any suitable distribution of functionality
between different functional units, processors or domains may be
used without detracting from the invention. For example,
functionality illustrated to be performed by separate processors or
controllers may be performed by the same processor or controller.
Hence, references to specific functional units are only to be seen
as references to suitable means for providing the described
functionality, rather than indicative of a strict logical or
physical structure or organization.
[0029] In various embodiments, the devices, instruments, systems,
and methods described herein may be used to detect one or more
types of biological components of interest. These biological
components of interest may be any suitable biological target
including, but are not limited to, DNA sequences (including
cell-free DNA), RNA sequences, genes, oligonucleotides, molecules,
proteins, biomarkers, cells (e.g., circulating tumor cells), or any
other suitable target biomolecule.
[0030] In various embodiments, such biological components may be
used in conjunction with various PCR, qPCR, and/or dPCR methods and
systems in applications such as fetal diagnostics, multiplex dPCR,
viral detection and quantification standards, genotyping,
sequencing validation, mutation detection, detection of genetically
modified organisms, rare allele detection, and copy number
variation. Embodiments of the present disclosure are generally
directed to devices, instruments, systems, and methods for
monitoring or measuring a biological reaction for a large number of
small volume samples. As used herein, samples may be referred to as
sample volumes, or reactions volumes, for example.
[0031] While generally applicable to quantitative polymerase chain
reactions (qPCR) where a large number of samples are being
processed, it should be recognized that any suitable PCR method may
be used in accordance with various embodiments described herein.
Suitable PCR methods include, but are not limited to, digital PCR,
allele-specific PCR, asymmetric PCR, ligation-mediated PCR,
multiplex PCR, nested PCR, qPCR, genome walking, and bridge PCR,
for example.
[0032] As described below, in accordance with various embodiments
described herein, reaction sites may include, but are not limited
to, through-holes, wells, indentations, spots, cavities, sample
retainment regions, and reaction chambers, for example.
[0033] Furthermore, as used herein, thermal cycling may include
using a thermal cycler, isothermal amplification, thermal
convention, infrared mediated thermal cycling, or helicase
dependent amplification, for example. In some embodiments, the chip
may be integrated with a built-in heating element. In various
embodiments, the chip may be integrated with semiconductors.
[0034] In various embodiments, the devices, instruments, systems,
and methods described herein may be used to detect one or more
types of biological components of interest. These biological
components of interest may include, but are not limited to, DNA
sequences, RNA sequences, genes, oligonucleotides, or cells (e.g.,
circulating tumor cells). In various embodiments, such biological
components may be used in conjunction with various PCR, qPCR,
and/or dPCR methods and systems in applications such as fetal
diagnostics, viral detection and quantification standards,
genotyping, sequencing validation, mutation detection, detection of
genetically modified organisms, rare allele detection, and copy
number variation.
[0035] TaqMan.RTM. Mutation Detection Assays can be used to
determine the mutation status for a given sample by running mutant
allele assays paired with a corresponding gene reference assay.
[0036] According to various embodiments described herein, to get
the quantitation information about mutants, each sample is tested
with two different assays, such as mutant assay for the mutation of
interests, and a reference assay which will cover both the
wild-type and mutant allele.
[0037] FIG. 2A illustrates an exemplary mutant allele assay 200.
The mutant allele assay is designed to mutations in the COSMIC db
to detect specific or multiple alleles. More specifically, an
allele-specific primer detects the mutant allele, while an MGB
oligonucleotide blocker suppresses the wild type allele. The assay
name may be Gene symbol_COSMIC ID_mu, e.g. KRAS_517_mu.
[0038] It should be recognized that corresponding wild type allele
assays are available for only a subset of the mutations. These can
be paired with their corresponding mutant allele assays.
[0039] FIG. 2B illustrates an example of a gene reference assay
202. Gene reference assay 202 detects a gene that target mutations
reside in. Here, a locus-specific primer pair amplify a
mutation-free region of the target gene. The assay name may be:
Gene symbol_rf, e.g. KRAS_rf.
[0040] There is often a high amount of wild-type background
template. To remedy this situation, the mutant assay is often
pushed to its limit for high specificity and additional component
is employed, of which the characteristics of PCR performance are no
longer typical. As a result, the PCR efficiency is often below 100%
leading to delays in Ct. According to the method described herein,
Ct data of the mutant (Ct.sub.mu) and Ct data from the reference
(Ct.sub.ref) are used. In this way, presence/absence information
and percentage of mutation are results are obtained.
[0041] The previously-used delta Ct method accounts for delayed Ct
values, but not the efficiency difference.
[0042] FIG. 3A illustrates an example plot of Ct versus input
quantity where the gene reference assay and the mutant detection
have the same efficiency and sensitivity. Here, Ct.sub.mu 302 can
be directly compared to Ct.sub.rf 304.
[0043] FIG. 3B illustrates an example plot of Ct versus input
quantity. In this example, as opposed to the example in FIG. 3A,
the efficiencies are the same, but sensitivities are different. In
this example, the Ct.sub.rf 308 was much earlier than the Ct.sub.mu
306 and corresponds to a higher input quantity. According to
embodiments described herein, the mutation percentage of the sample
may be calculated by the following equation:
Mutation %=2.sup.-(Ct.sup.mu.sup.-Ct.sup.rf.sup.)
[0044] FIG. 4 illustrates another example plot of Ct versus input
quantity. In this example, the both the efficiencies and
sensitivities are different. This is the typical scenario for
mutant assays. The previously-used delta Ct method would not work
with assays such as the ones used in FIG. 4.
[0045] Generally, according to embodiments described herein, each
sample will be run with two different assays: one is mutant
specific, the other is for gene specific which will be used as
denominator for percentage calculation.
[0046] The existing quantitation method relies on a pre-calculated
value that's provided by us, inherent .DELTA.Ct. The purpose is to
control the difference between the two different assays. It is
generated with a fixed amount of template for each assay.
Mutant
percentage=0.5.sup.((Ct.sup.mu.sup.-Ct.sup.rf.sup.)-.DELTA.Ct.sub-
.inherent)*100%
[0047] The inherent .DELTA.Ct is effective to capture one aspect of
the differences between the two assays. Briefly, the existing
method is not effective for sample and assay combination away from
the condition that inherent .DELTA.Ct was generated, such as sample
amount and the PCR efficiencies away from the expected 100%.
[0048] According to other embodiments of the present teachings, a
quantitation curve may be generated. FIG. 5 illustrates a plot of
Ct versus relative quantity. Mutant percentage is a type of
relative quantitation. By running a series of dilutions of a
calibrator, with known ratio between mutant and reference assay
target, a ratio of unknown sample can be deduced. This is because
the initial concentration of the calibrator is no longer
relevant.
[0049] FIG. 6 illustrates a quantitation curve according various
embodiments described herein. FIG. 6 illustrates a plot of the Ct
and the dilution ratio (in log 10). Ct.sub.mus 602, 606, 610, and
614 are plotted for dilutions of 0.001.times., 0.01.times.,
0.1.times., and 1.times., respectively. Similarly, Ct.sub.rfs 604,
608, 612, and 616 are plotted for dilutions of 0.001.times.,
0.01.times., 0.1.times., and 1.times., respectively. As such, the
curves illustrated in FIG. 6 may be used to determine a quantity of
an unknown sample.
[0050] FIG. 7 illustrates data to support the performance of the
quantitation method according to various embodiments described
herein.
[0051] FIG. 8A and FIG. 8B illustrate several assays of the Von
Hippel-Lindau tumor suppressor, an E3 ubiquitin protein ligase.
FIG. 8A illustrates a plot of detected mutant percentage versus an
expected mutant percentage using commonly used methods. On the
other hand, FIG. 8B illustrates a plot of detected mutant
percentage versus an expected mutant percentage according to
various embodiments described herein. Independent of the assays, it
is seen that the method according to embodiments of the present
teachings lead to closer detected mutant percentages with respect
to the expected mutant percentages (FIG. 8B) as compared with
detected mutant percentages determined by the delta Ct method
versus the expected mutant percentages (FIG. 8A).
[0052] Similarly, FIGS. 9A and 9B illustrate an improvement of
accuracy using the method according to embodiments described herein
versus the delta Ct method. Both FIG. 9A and FIG. 9B illustrate the
deviation of expected mutant percentage compared with the expected
mutant percentage. FIG. 9A illustrates the deviation from expected
mutation percentage using mutation percentages determined by the
delta Ct method. On the other hand, FIG. 9B illustrates the
deviation from expected mutant percentage from mutation percentages
determined by methods according to embodiments of the present
teachings. The deviation is much less using the method of the
present teachings (FIG. 9B) compared with the deviation using the
delta Ct method (FIG. 9A)
[0053] Although the present invention has been described with
respect to certain exemplary embodiments, examples, and
applications, it will be apparent to those skilled in the art that
various modifications and changes may be made without departing
from the invention.
* * * * *