Effects of size, cooperativity, and competitive binding on protein positioning on DNA.

Accurate positioning of proteins on chromosomal DNA is crucial for its proper organization as well as gene transcription regulation. Recent experiments revealed existence of periodic patterns of nucleoprotein complexes on DNA, which frequently cannot be explained by sequence-dependent binding of proteins. Previous theoretical studies suggest that such patterns typically emerge as a result of the proteins' volume-exclusion effect. However, the role of other physical factors in patterns' formation, such as the length of DNA, its sequence heterogeneity, and protein binding cooperativity/binding competition to DNA, remains unclear. To address these less understood yet important aspects, we investigated potential effects of these factors on protein positioning on finite-size DNA by using transfer-matrix calculations. It has been found that upon binding to DNA, proteins form oscillatory patterns that span over the length of up to ∼10 times the size of the protein binding site, with the shape of the patterns being strongly dependent on the length of DNA and the proteins' binding cooperativity to DNA. Furthermore, calculations showed that small variations in the proteins' affinity to DNA due to its sequence heterogeneity do not much change the main geometric characteristics of the observed protein patterns. Finally, competition between two different types of proteins for binding to DNA has been found to lead to formation of highly diverse and complex alternating positioning of the two proteins. Altogether, these results provide new insights into the roles of physicochemical properties of proteins, the DNA length, and DNA-binding competition between proteins in formation of protein positioning patterns on DNA.