Position-specific Scoring Matrix - Information Content of A PWM

Information Content of A PWM

The information content (IC) of a PWM is sometimes of interest, as it says something about how different a given PWM is from a uniform distribution.

The self-information of observing a particular symbol at a particular position of the motif is:

The expected (average) self-information of a particular element in the PWM is then:

Finally, the IC of the PWM is then the sum of the expected self-information of every element:

Often, it is more useful to calculate the information content with the background letter frequencies of the sequences you are studying rather than assuming equal probabilities of each letter (e.g., the GC-content of DNA of thermophilic bacteria range from 65.3 to 70.8, thus a motif of ATAT would contain much more information than a motif of CCGG). The equation for information content thus becomes

where is the background frequency for that letter. This corresponds to the Kullback-Leibler divergence or relative entropy. However, it has been shown that when using PSSM to search genomic sequences (see below) this uniform correction can lead to overestimation of the importance of the different bases in a motif, due to the uneven distribution of n-mers in real genomes, leading to a significantly larger number of false positives.