Pseudocounts for transcription factor binding sites

To represent the sequence specificity of transcription factors, the position weight matrix (PWM) is widely used. In most cases, each element is defined as a log likelihood ratio of a base appearing at a certain position, which is estimated from a finite number of known binding sites. To avoid bias due to this small sample size, a certain numeric value, called a pseudocount, is usually allocated for each position, and its fraction according to the background base composition is added to each element. So far, there has been no consensus on the optimal pseudocount value. In this study, we simulated the sampling process by artificially generating binding sites based on observed nucleotide frequencies in a public PWM database, and then the generated matrix with an added pseudocount value was compared to the original frequency matrix using various measures. Although the results were somewhat different between measures, in many cases, we could find an optimal pseudocount value for each matrix. These optimal values are independent of the sample size and are clearly correlated with the entropy of the original matrices, meaning that larger pseudocount vales are preferable for less conserved binding sites. As a simple representative, we suggest the value of 0.8 for practical uses.