Biology Reference
In-Depth Information
To understand the possible mechanisms for such noise
behavior as shown in eq. (3), it is convenient to translate the above
noise strength in q (
=
log 10 ( E )) to the noise strength in intensity
, where E 0 =
10 q 0
2
2
2
2
2
and
EE
:
σ
(
)
K < ≈
δ
E
(ln/)
10
2
E
<>
δθ
E
0
dE
E 0 . By using the numerical fit for s prep , the variance of the
sample preparation noise dE prep , s E, prep , can written as
=
E
2 ,
2
3
2
σ
()
E
K
δ
E
≈×
19 10
.
E
+
012
.
E
(4)
prep
0
prep
0
The two terms in eq. (4) represent two independent sources of noise,
the discussion of which follows.
For the first term, d E prep is proportional to the gene expression E 0 itself.
To understand this term, it is important to realize that during sample
preparation the mRNA is first reverse transcribed into cDNA, and cRNA
is subsequently generated from cDNA by IVT. The number of RNA
molecules is amplified during the IVT, that is, N cRNA
N mRNA ,
where A is the amplification rate and N mRNA and N cRNA are the num-
bers of mRNA and cRNA molecules, respectively. A varies between
one sample preparation process and another due to fluctuations in the
reaction conditions, including fluctuation due to handling of the sample
(“human factors”). The fluctuation of A between different sample
preparation processes, denoted as d A , leads to a fluctuation in N cRNA
of the form d A
=
A
×
N mRNA . Since N mRNA is proportional to E 0 , the first
term in eq. (4) can thus be explained by the fluctuation in A .
Furthermore, s A , the standard deviation of A , can be estimated:
×
, where A is the mean amplification
rate. Assuming a typical value of A around 100 [5], one has s A
K <>≈×
212
/
312
/
σδ
A
(.
19 10
)
A
A
4.4.
For the second term in eq. (4), d E prep is proportional to the square
root of E 0 , indicative of Poisson-like noise. Such noise in the sample
preparation may arise naturally from the probabilistic nature of the
amplification process (IVT).
The accuracy of the sample preparation process inevitably depends
on “human factors,” whose influence is difficult to estimate. The result
here can be best viewed as an upper limit for the noise caused by the
intrinsic chemical processes involved in the sample preparation.
Most of the total measurement error comes from the hybridization
noise, which depends strongly on the expression level (see figure 4.4).
For expression level q
the hybridization noise dq hyb decreases
rapidly with increasing expression level as shown in figure 4.5, where
log 10 (s hyb ) is plotted versus q 0 . Empirically, s hyb can be fitted by:
0 ≥ 1,
2
≈× −γ
q
sqb
()
10
0
0
hyb
with b
=
1.6
±
0.2 and g
=
1.1
±
0.1 for the region 1.4
q 0
2.7, before
saturating to a constant 1.1
×
10 −3 .
Search WWH ::




Custom Search