Hardware Reference
In-Depth Information
Y
k
P.G
\
A
k
/
D
.1
p
i
/
P.G/
(5.2)
i
D
1
If no signal is detected at the kth thermal cycle, the conditional probability that
“this is a good droplet” (written as P.G
j
A
k
/) is defined as the quotient of the joint
probability of G and A
k
, and the probability of A
k
:
P.G
\
A
k
/
P.A
k
/
P.G
j
A
k
/
D
P.G
\
A
k
/
P.G
\
A
k
/
C
P.G
c
\
A
k
/
D
(5.3)
i D1
k
.1
p
i
/
P.G/,andP.G
c
\
A
k
/
D
P.G
c
/
D
1
P.G/.
where P.G
\
A
k
/
D
Therefore, we have:
i D1
k
.1
p
i
/
P.G/
P.G
j
A
k
/
D
i D1
k
.1
p
i
/
P.G/
C
1
P.G/
1
P.G/
P.G
c
j
A
k
/
D
:
i D1
k
.1
p
i
/
P.G/
C
1
P.G/
5.2.3
An Improved Statistical Model for Amplification of DNA
During the calibration of DNA amplification, one may categorize the droplets based
on the number of DNA strands therein. Equation (
5.3
) remains valid in this scenario.
Let event G
i
denote “a droplet with i DNA strands is dispensed into the biochip”.
We assume that M
min
is the minimum number of DNA strands in a droplet needed to
run DNA amplification successfully. Then the event G in (
5.3
) can be expressed as:
G
D
G
M
min
[
G
M
min
C1
[
G
M
min
C2
[[
G
1
;
(5.4)
where the events G
M
min
, G
M
min
C1
,
, G
1
are mutually exclusive.
The event A
k
in (
5.3
) can now be written as:
A
k
D
A
k
[
A
k
[
A
k
[
A
k
[[
A
k
;
(5.5)
