Noise Induced Regulation of DNA Loops

Protein-mediated DNA loop formation is a ubiquitous means of regulating gene transcription. Loop formation in ds-DNA is driven by tiny forces on the order of fN arising from thermal fluctuations within the intracellular environment. Surprisingly, these forces are much smaller than the typical piconewton forces that arise from various intracellular processes, such as the procession of molecular motors or DNA-cytoskeletal attachments. This has led to theoretical predictions, and a recent experimental confirmation by our lab, that forces as small as a few hundred femtonewtons can severely reduce the rate of loop formation.We further explore the utility of using tension as a regulatory mechanism by asking how this mechanism is effected by noise. From empirical data that we have collected on loop formation rate as a function of substrate tension, we develop an effective potential that reproduces the loop transition rates given by the mean-first passage time of escape from the potential. We next incorporate this effective potential into a stochastic model of DNA subjected to an applied, fluctuating force.The theory predicts a strong enhancement in the rate of loop formation under increasing levels of noise and, when normalized to the noise free rate, displays a universal behavior relatively independent of the mean force. This suggests that applying a varying level of tension to the DNA may be a robust method for regulating transcription. We then compare the theory with an experiment performed in our lab where we have subjected DNA, capable of forming LacI mediated loops, to a fluctuating force by means of axial optical tweezers.