In the example above, without pseudocounts, any sequence which did not have a in the 4th position or a in the 5th position would have a probability of 0, regardless of the other positions. Conversion of position probability matrix to position weight matrix Most often the elements in PWMs are calculated as log likelihoods. That is, the elements of a PPM are transformed using a background model so that: describes how an element in the PWM (left), , can be calculated. The simplest background model assumes that each letter appears equally frequently in the dataset. That is, the value of for all symbols in the alphabet (0.25 for nucleotides and 0.05 for amino acids). Applying this transformation to the PPM M from above (with no pseudocounts added) gives: The entries in the matrix make clear the advantage of adding pseudocounts, especially when using small datasets to construct M. The background model need not have equal values for each symbol: for example, when studying organisms with a high GC-content, the values for and may be increased with a corresponding decrease for the and values. When the PWM elements are calculated using log likelihoods, the score of a sequence can be calculated by adding (rather than multiplying) the relevant values at each position in the PWM. The sequence score gives an indication of how different the sequence is from a random sequence. The score is 0 if the sequence has the same probability of being a functional site and of being a random site. The score is greater than 0 if it is more likely to be a functional site than a random site, and less than 0 if it is more likely to be a random site than a functional site. The sequence score can also be interpreted in a physical framework as the binding energy for that sequence. Information content 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