Our results suggest how a force dependent genetic switch that employs DNA looping to regulate transcription could operate stably within a noisy environment. For instance, consider a regulatory element controlled by the formation of a DNA loop at a basal rate k$_{t}$$_{1}$ under constant tension h$_{1}$ . A regulatory signal could be provided by a change in tension, h$_{2}$ , such that the loop formation rate is now a factor of p times the basal rate, i.e. k$_{t}$$_{2}$/k$_{t}$$_{1}$ = p . If we assume that the tension felt by the DNA fluctuates around the targets t$_{1}$ and t$_{2}$ such that we have two new looping rates ˜ k$_{t}$$_{1}$ and ˜ k$_{t}$$_{2}$ , our results imply that ˜ k$_{t}$$_{1}$/k$_{t}$$_{1}$ = ˜ k$_{t}$$_{2}$/k$_{t}$$_{2}$ , which means that ˜ k$_{t}$$_{2}$/ ˜ k$_{t}$$_{1}$ = p , so that the expression signal is unaffected by the noise. 

We have demonstrated how noise from thermal and environmental fluctuations drives protein-mediated DNA loop formation, yet leaves the loops unaffected once formed. En- vironmental fluctuations only a fraction of the size of thermal fluctuations in the DNA can greatly enhance the rate at which these loops form. We interpret these results with a fluctuating barrier model that can quantitatively explain and predict our measurements. This model is based on the previously demonstrated sensitivity of loop formation to static mechanical tension, which led to the suggestion that cells may utilize tension to regulate transcription through mechanical pathways, as opposed to the more commonly considered biochemical ones [7]. Based on our new observations, we may now postulate the feasibility of an alternate mechanical regulatory mechanism that uses environmental fluctuations as a means to control transcription. The rate enhancement of fluctuations might, in fact, explain why a simple loop results in several hundred fold repression in vivo [5], even though the looped and unlooped states have roughly equal lifetimes in vitro . Furthermore, we have shown that the sensitivity of loop formation to fluctuations is insensitive to baseline static mechanical tension, and have demonstrated how this feature can lead to a robustness in regulatory function. 

*Y. F. Chen and J. N. Milstein contributed equally to this work. We thank Jason Kahn for the LacI protein and David Wilson for help with the modeling. This work was supported by NIH, Grant No. GM65934, and NSF FOCUS, Grant No. 0114336. 

