Global Gene Expression Assays: Quantitative Noise Analysis - Systems Biology: Networks, Models, and Applications - page 111

p (, qqq ) K P ( dqq ) d dq

∫ (5)

120 dq ≥∆ q 2 0

0

∆ qqq

0

=− / 2

where 1, one can use

eq. (2), and the p -value can be expressed simply as a function of the
signal to noise ratio

and

qqq
0

=+ ( )/ 2

. For q 0 ≥

1 2 1 2

∞

K K

R ∆ qsq /(): p (, qqq ) 2 Φ () x dx .

∫

020 120

R

q 0 ) = 0.05 are shown
together with two lines corresponding to a uniform 2-fold expression
value change

In figure 4.6, the contour lines for p (q 1 ,q 2 |

[ q 12 −= log 2 ]

. This clearly shows that, given a fixed

confidence level ( p -value 0.05), a requirement of a uniform 2-fold

expression change is at once too stringent for high expression levels
and inadequate for the low expression levels (q 0 ≤

=

2). In fact, given the
strong expression level dependence of the noise, no significance crite-
rion based solely on the expression fold change is appropriate. Instead,
in order to guarantee a fixed level of statistical relevance p 0 , one should
enforce a uniform (i.e., expression level independent) lower bound on
the signal to noise ratio R ≥ R 0 ( p 0 ).

QUANTITATIVE NOISE ANALYSIS OF MPSS EXPERIMENTS

The data and results presented in this section are largely derived from the
quantitative study of noise in MPSS experiments presented in ref. [13],

Figure 4.6 The contour line of p -value equal to 0.05. Any pair of expression
values (q 1 ,q 2 ) outside the shaded area represent differentially expressed genes
beyond experimental noise with a p -value of 0.05 or smaller. The two dotted
lines represent 2-fold expression changes.