2.3 Results
2.3.2 Measuring gene expression
Precision of measurements
Precision of RNA-Seq results is affected by the number of times a library is measured (reflected in the reads produced) and by the abundance of each transcript. In order to measure the precision of the RNA-Seq results, we categorized transcript reads by abundance: not expressed, expressed below threshold (0.25 RPKM, discussed in the next section), and between the intervals of 0.25, 3, 30 and 300.
Figure 2.2 shows the large difference between the numbers of reads coming from the most abundant transcripts and those from moderately abundant transcripts. In a cDNA library prepared for RNA-Seq analysis of the densin knockout mouse, half of the library is composed of copies of just 7 percent of transcripts. Consequently, a random sample of transcripts will contain many examples of the most abundant transcripts, which are thus sequenced more frequently. More abundant transcripts will therefore be measured with greater precision than less abundant ones.
In order to understand the effects of the predominance of abundant transcripts on the precision of the experiment, we assessed the precision of this data set by combining reads from three sequencing runs of a single library in random order. We then calculated transcript abundance from the first four million reads, from the first eight million reads, and so on for each increment shown in Table 2.2. For each
0.25-3 3-30
30-300 300+
(a) Sequencer reads grouped by tran- script abundance (RPKM)
0
0-0.25 0.25-3 3-30
30-300 300+
(b) Genes grouped by transcript abun- dance (RPKM)
Figure 2.2: Seven percent of transcripts account for over half of all reads. Tran- scripts were categorized by abundance: Not expressed (0 RPKM), expressed below threshold (0<x<0.25), and expressed between the intervals of 0.25, 3, 30 and 300, intervals chosen for comparison with Mortazavi et al. (2008). Plot (a) illustrates the fraction of the sequencer reads from wild-type mouse forebrain by each abundance category. Plot (b) illustrates the fraction of mRNA-producing genes corresponding to each abundance categories. The orange segment in (a) shows fifty-one percent of all reads are derived from transcripts with an abundance measurement between 30 and 300 RPKM. However, those transcripts comprise only seven percent of mRNA- producing genes.
increment, we noted the number of measurements that were within 5 percent of the final value: the measurement calculated with all the reads available for that sample.
Table 2.2 shows an example of the measurements for a single gene,Gabra2, which codes for the GABAAR subunit α2. The abundance of the Gabra2 transcript is within 5 percent of its final value (6.39 RPKM) when 8, 28, 32 or 36 million reads are included in calculations. Many genes show a trend like this, increasing precision as the measurement is based on more reads.
The fraction of all transcripts within 5 percent of their final value is plotted against the number of reads used to calculate the abundance in Figure 2.3. More highly abundant transcripts are precisely measured with fewer reads, as indicated by the blue and purple lines. Of all transcripts expressed above 3 RPKM, 99 percent are
Table 2.2: The abundance measurements of the γ-aminobutyric acidAreceptor subunitα2 transcript are increasingly precise as more reads are included in the calculation.
Million reads
use in calculations 4 8 12 16 20 24 28 32 36 40
Transcript abundance
(RPKM) 6.89 6.61 5.74 5.75 5.89 6.07 6.09 6.1 6.28 6.39
Percent final value 107.8 103.4 89.8 90.0 92.2 95 95.3 95.5 98.3 100.0
within 5 percent of their final abundance measurement (indicated by the green, blue and purple lines). Thus we conclude that by pooling our samples we have sufficient depth of sequencing to analyze genes that are expressed at greater than 3 RPKM.
Measurements of known quantities of transcripts
In order to determine the number of transcripts represented by one RPKM, we added reference transcripts to our samples and compared the resulting transcript abundance measurements to the known concentrations. The seven reference transcripts, derived from Arabidopsis and phage lambda, ranged in length from 325 to 11,936 bases and in concentration from 50,000 to 500 × 108 transcripts per 100ng of experimental transcripts. The measured abundance is highly correlated with the number of tran- scripts. One RPKM corresponds, on average, to 150,000 transcripts (Figure 2.4). The high correlation and small error indicates that RPKM is a consistent measure of the number of samples in a transcript and that measurements are linear across different transcripts.
Million reads included in measurement Fraction of trancripts within 5% of final value 00.20.40.60.81
0 4 8 12 16 20 24 28 32 36 40
RPKM 300+
30-300 3-30 1-3 0-1
Figure 2.3: Transcripts more abundant than 3 RPKM are precisely measured. The abundance of each transcript was calculated with increasing numbers of sequencer reads. Precise measurement was defined as a measurement within 5 percent of the final value, and transcripts were grouped by abundance category. For each increment of reads, the fraction of precise measurements for an abundance category was plotted against the number of reads used in the calculation. Ninety-nine percent of transcripts more abundant than 3 RPKM are precisely measured to within 5 percent of their final value.
To estimate the noise in the measurements, we considered the transcript levels that are reported not to be expressed in brain: Hnf4a, Myf5, Myf6, Myod1, and Myog.
The average transcript level for these five genes was 0.025 RPKM. We used a ten- fold increase of that threshold, 0.25, as a conservative threshold of expression when evaluating patterns of expression in the entire transcriptome. Because of the results
Number of transcripts added to sample 1
10 100 1000 10000
5e+04 5e+05 5e+06 5e+07 5e+08
Transcript level (RPKM)
R2 = 0.991 AGP
AP2 EPR1
Lambda 1-1
Lambda 2-3
OBF5 VATG
Figure 2.4: Validation of RPKM as a consistent unit of measure. The measured transcript abundance, in RPKM, is plotted against the number of known Arabidopsis and phage lambda reference transcripts. Seven different reference transcripts were added to mouse brain samples and sequenced together with the mouse brain transcripts. The measured transcript abundance of these transcripts is highly linearly correlated with the number of reference transcripts spiked in to the sample (R2=0.991). The red line indicates where 1 RPKM consists of 150,000 transcripts. Error bars indicate standard error of the mean.
The high correlation and small error indicates that RPKM is a consistent measure of the number of samples in a transcript. Reference transcripts were measured in the four forebrain samples.
of our precision analysis, we limited analysis of transcript abundance of individual genes to those expressed over 3 RPKM in either of the compared samples.
Range of gene expression levels within a single animal
The RNA-Seq measures the abundance of each transcript in a sample. We measured the abundance of 33,114 transcripts in samples from 10 mice. In the forebrain samples
from the wild-type mice, 10,625 of the 33,114 transcripts considered are not expressed (zero RPKM). Another 5,749 are expressed below threshold (0.25), calculated as described in section 2.3.2. There are 16,737 transcripts above threshold.
Figure 2.5 presents an overview of the distribution of the transcript abundance in the forebrain of wild-type mice. Transcript measurements were binned, and the log of the number of genes in each bin is indicated on the ordinate. For clarity, 5 genes with RPKM above 1000 were omitted. The histogram shows that majority of transcript levels are less than 50 RPKM (31,822 transcripts). The distribution of RPKM values is heavily skewed toward lower values. As expression levels increase, the number of genes expressed at that level drops.
Figure 2.6 shows the data depicted in 2.5 at higher resolution, focussing on the distribution of transcripts expressed between the lower threshold, 0.25, and twenty RPKM. The transcript measurements are binned, and the number of genes in each bin is indicated on the ordinate. Transcript levels represented in this plot were measured in the forebrains of wild-type mice. Together, Figures 2.5 and 2.6 show that most genes that are expressed in forebrain are expressed at less than 20 RPKM.