difference between the potential energy of a worm-like chain (WLC) and the work done by tension: where l$_{l}$ is the loop length of the DNA and x is the relative extension of the DNA in units of l$_{p}$ . We can now calculate the characteristic time necessary to form a loop under an applied force using the principle of detailed balance where τ$_{0}$ is the characteristic time at zero force. X-ray studies of the co-crystals of LacI protein bound to short operator fragments have revealed the structure of the DNA protein complex [12]. These results impose constraints upon, but do not fully determine the topology of the DNA loop. The preferred direction in which the DNA enters and leaves the looped complex remains unsettled, but the correspond- ing topologies are either anti-parallel conformations, with a kink angle of approximately 150 ◦ , or parallel conformations, with a kink angle of 30 ◦ . To fit the data, we calculate τ$_{f}$ = 1 /k$_{L}$ from Eq. 9 as a function of force using the WLC model to provide the relative extension x in Eq. 8. Since we cannot directly measure the force free lifetime τ$_{0}$ , we use this as a single adjustable parameter to fit the curves. The value for τ$_{0}$ is given by a least squares fit to the data. We then generate a curve for both the anti-parallel and parallel conformations and see, from Fig. 3, that the anti-parallel topology is more force-sensitive than its parallel counterpart. Our data suggest that the anti-parallel conformation is the dominant topology of a generic LacI-mediated DNA loop. In conclusion, our results establish that very small forces, on the order of a hundred femtonewtons, can control the assembly of the regulatory protein-DNA complex necessary for expression of the lac gene. On the other hand, once formed, the looped complexes are quite stable and cannot easily be disrupted by tension in the substrate DNA, giving the system much- needed robustness. Thus, it appears more than likely that mechanical pathways can control transcription through the application of tiny forces that are generated by other intracellular processes. We hope that the development of force measurement techniques inside living cells will lead to the identification of such pathways. We also conclude that such regulatory forces would likely act on the assembly process of these complexes, but not their breakdown. 8 τ$_{f}$ τ$_{0}$ = e $_{−}$Δ $^{F}$, (9) F$_{S}$ = $_{−}$l$_{l}$ x 2 4 ( 1 (1 − x ) 2 + 2 ) , (8)