Calculating transcriptional drift and drift-variance

Transcriptional drift (td) is the change in transcript level of a gene at a given age from its level in young animals (“young reference”). As all the subsequent calculations depend on the age chosen for “young reference” we made sure to indicate the age used as a “young reference” for each plot (see below). For all the C. elegans work, the “young reference” age was day 1, at the onset of reproductive maturity in adulthood.

For any gene x, transcriptional drift (td) is defined as (Equation 1).

or, which is the same as

where, ‘cpm’ stands for counts per million; ‘t’ stands for time in days, weeks or years, dependent on the organism.

Equation 1 normalizes the level of transcription for all genes to 0 for a young animal. Note: If several biological replicates are available for the age of the young reference, a variance for the young age can be calculated (see the section below titled ‘Variance for “the young reference”’).

To evaluate changes in co-expression, we calculated the drift-variance (dv) (Equation 3) over a group of n genes with transcriptional drift-values ranging from td_i=1 to td_n.

Thus, if genes maintain a youthful co-expression pattern, drift-variance stays relatively small. If large fractions of genes within a GO or an entire transcriptome change expression in opposing directions, the drift-variance increases, suggesting a loss of youthful co-expression patterns as shown in Figure 1h,i.