Example: Lac Looping

The lac repressor (LacI) represses the transcription of the E. coli lac operon which allows metabolism of the sugar lactose. LacI binds two of three sequences on the genome; here we consider the case in which the O2 and O3 sites are bound, which have about 400 bp of intervening DNA between them. The LacI protein itself consists of two arms, and it may be that those arms can flexibly swing open and closed to accommodate the DNA. Here we plot the probability density as a function of the angle of each arm: an angle of 90 degrees is the case where the arms are splayed wide apart. The wormlike chain model predicts that binding is easiest when each arm is at an angle of approximately 60 degrees (the angle between the two arms is 120 degrees).