FIG. 3: Measured values for k$_{−}$ ( △ ), k$_{+}$ ( ⋄ ), k$_{L}$ ( ■ ), and k$_{U}$ ( ◦ ) (see Table 2). The looping rate k$_{L}$ is fit by the theoretical predictions for the anti-parallel (solid line) and parallel (dashed line) topologies illustrated in the insert. TABLE II: Rates extracted from kinetic rate equations. Force (fN) 60 ± 5 78 ± 6 121 ± 9 183 ± 15 Kinetic Rates (10 $^{$_{−}$3}$/s ) k$_{U}$ 48 . 1 ± 0 . 6 44 . 5 ± 0 . 4 41 . 5 ± 0 . 6 40 ± 1 k$_{L}$ 262 ± 7 196 ± 6 79 ± 1 32 ± 1 k$_{−}$ 61 ± 9 48 ± 5 21 ± 2 25 ± 4 k$_{+}$ 40 ± 10 24 ± 5 14 ± 2 21 ± 3 We thank Jason Kahn for providing us with the LacI protein. This work was supported by the National Institutes of Health, Grant No. GM65934, and the National Science Foundation FOCUS, Grant No. 0114336. 9 [1] F. Jacob and J. Monod, J. Mol. Biol. 3 , 318 (1961); M. Lewis, C. R. Biol 328 , 521 (2005); C. J. Wilson, H. Zhan, L. Swint-Kruse, K. S. Matthews, Cell. Mol. Life Sci. 64 , 3 (2007). [2] S. Oehler, E. R. Eismann, H. Kr¨ amer, and B. M¨ uller-Hill, EMBO J. 9 , 973 (1990); J. M. G. Vilar and S. Leibler, J. Mol. Biol. 331 , 981 (2003). [3] K. S. Matthews, Microbiol. Mol. Biol. Rev. 56 , 123 (1992). [4] L. Finzi and J. Gelles, Science 267 , 378 (1995); F. Vanzi, C. Broggio, L. Sacconi, and F. S.