To perform the screening, it is first assumed that fragmented RNAs are randomly distributed along the entire pre-tRNA; that is, the RNAs are uniformly distributed across the entire length of pre-tRNA. According to this assumption, we could conclude that, of the entire length of tRNA, the probability of one small-RNA fragment mapped onto one particular position in the tRNA is

where *L* is the length (in nucleotide, *nt*) of the tRNA, and *l* is the length (in nucleotide, *nt*) of the small RNA fragment being mapped onto the tRNA.

Therefore, the probability of more than k (inclusive) small RNA fragments mapped onto the same position in the tRNA follows the Binomial distribution, and the probability for this event is

where *k* is the observed counts of small RNA fragments mapped onto that particular position in the tRNA, and *n* is the total number of fragments mapped onto the entire tRNA.

If there are more than *k* (inclusive) small RNA fragments mapped onto one particular position in the tRNA, but the probability of this event occurring by chance (Eq. 2) is less than 1% (referred to the *p*-value, and can be adjusted to your satisfaction), then we could conclude that the assumption above is false (with 99% confidence, by default); *i.e.*, this event does not occur by chance.

Note, however, that generally tRFs is of more than 16 *nt* in length. To take this fact into consideration, we should ensure that the tRFs candidate matches with tRNA sequence for consecutive more than 16 *nt*. (Mismatches, indels are allowed.) This, in turn, corresponds to the requirements that there are at least 16 *nt* bases in consecutive position in tRNA (which matches with the candidate tRFs sequences) should have a *p*-values less than 1%. (Figure 2)

**Figure 2. Schematic demonstration of how the core algorithm works.**

*n* is the sum of the reads mapped to the tRNA, *k* is the sum of the reads that are mapped to the particular position in the tRNA. *l* is the length of the reads, and *L* is the length of the tRNA. By default, a tRF candidate corresponds to more than 16 contiguous nucleotides with *p*-value(s) less than 0.01.