The evolutionary selection of DNA base pairs in gene-regulatory binding sites

The DNA base-pair sequences that serve as gene-regulatory sites have been selected during evolution to provide an appropriate functional binding for a particular protein. In most cases, the function depends on the binding probability, which can be influenced both by the binding strength and by the abundance of the protein in the cell. As a consequence, the same function can be achieved with strong binding sites and a small amount of protein as with weak binding sites and a large amount of protein. However, increasing the protein burden will decrease the growth rate of the cells, even when all functions remain the same. Thus, for maximal growth, the protein levels should be as low as possible and the binding correspondingly strong. On the other hand, sequences with a weaker binding can be formed in many more ways and are, therefore, more probable, and random mutations are more likely to produce them. Thus, the selection pressure against an increased protein burden can be balanced against the random mutational drift in the recognition sequences, thereby tying together the statistics of base-pair choice, the binding strength, and the protein burden. In terms of this model, the selection pressure can be estimated from the properties of a gene-regulatory protein and its recognition sites. A key feature is the mutational randomization pressure that appears as a fundamental force shaping the optimal solutions that provide maximal growth. The model is tested on a number of gene-regulatory systems in Escherichia coli. The same principles should hold for all proteins for which overall activity in the cell is proportional to abundance; then the selective pressure to increase the efficiency of an individual protein cannot be larger than the selective pressure to decrease the total protein burden.