τ and τ, which represent the time-averaged single-molecule rates of I II and II I transitions

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1 Supporting nformation To Single-Molecule Study of Metalloregulator CueR DNA nteractions Using Engineered Holliday Junctions Nesha May Andoy, Susanta K. Sarar, Qi Wang, Debashis Panda, Jaime J. Benítez, Alesandr Kalininsiy, and Peng Chen * Department of Chemistry and Chemical Biology, Cornell University, thaca, New Yor 853, U.S.A. * To whom correspondence should be address; pc5@cornell.edu. Derivation of the single-molecule inetics of the structural dynamics of HJC A. Free HJC The structural dynamics of a HJ, if measured at the single-molecule level at tens of milliseconds time resolution, follows a two-state inetics effectively: where denotes conf- and denotes conf- see also Figure in the main tex. The waiting time in the trajectories is the time needed to complete transition; the waiting time is to complete transition; both are simple one-step inetic reactions. The probability density functions for and, f ) and f ), are both single-exponential functions, with f ) exp ) and f ) exp ). The inverse of the average waiting times, and, which represent the time-averaged single-molecule rates of and transitions respectively, are: A) f )d B. Apo-CueR and HJC interactions A) f )d The inetic mechanism of apo-cuer interactions with HJC is shown in Figure 5A. The inetic processes happening during are the following inetic steps: S

2 P- [P] The corresponding single-molecule rate equations are: / dt P B) / dt + [P]) P + P P- B) - / dt [P] P P P- B3) where P s are the probabilities of finding HJC in the corresponding states at time t and s are the rate constants for the transitions. At the on-set of each, i.e., right after a transition, the first state that HJC reaches is ; so the initial conditions for solving the above differential equations are: P ), P ), P - ), where t being the on-set of each. And at any time, P + P + P. P- We can then evaluate the probability density function of, f ). The probability of finding a particular is f ) Δ, which is equal to the probability for HJC to switch from to between and + Δ, Δ P ), ). Therefore, f ) Δ ΔP ). n the limit of infinitesimal Δ, f ) is equal to ) d. Solving for P ) using equations B-B3 by Laplace transform, the probability density function of is: α + β ) e α α f ) [ α + e ) + β + ) e )] α + + where α + + [P]) and β [P]). Then: / f )d + [ P] K P where K P is the dissociation constant for the apo-cuer conf- complex. This equation is given as Eq. in the main text. The inetic processes happening during are the following inetic steps: P- [P] [P] P - S

3 The corresponding single-molecule rate equations are: / dt P + P B) 6 P- / dt + [P]) P + P P- B5) / dt [P] P + + [P]) P P ) B6) P- 6 5 P- + 5 P - t P - / dt 5[P] PP- 5P P - B7) The initial conditions for solving above equations are: P ), P ), P - ), and P ). And at any time, P + P + P + P. Similarly, f ) ) / d. P - Using equations B-B7 to solve for ) where K P- + 6 ) / P- P - P, we can obtain f ) f )d + [P]/ K P- 6 + [P]. Then, + [P]/ K / K P- P- K P - ) and K 5 5. This equation is given as Eq in the main text. P C. Holo-CueR and HJC interactions. The inetic mechanism for holo-cuer HJC interactions is shown in Figure 5B. The inetic processes happening during are: [P] P- 3 The corresponding single-molecule rate equations are: / dt P + P C) 3 P- / dt + [P]) P + P P- C) / dt [P] P + ) P C3) P- 3 P- ) ) ) ) / d The initial conditions are P, P and P - ) and at any time, P + P + PP-. Similarly, f, and solving equations C-C3 for P ), we can obtain f ), and where K P- + 3 ) / f )d + [P] 3 / K + [P]/ K P- P-. This equation is given as Eq. 3 in the main text. The inetic processes happening during are: S3

4 P- [P] 6 5 P - 5 [P] 7 The corresponding single-molecule rate equations are: / dt P + P + P ) C) 6 P- 7 P- t / dt + [P]) P + P P- P - / dt [ P] P [P]) PP- + 5P P - P - / dt 5[ P] P 5 7 ) PP - P + ) ) P - ) + P + PP- + PP - C5) C6) C7) The initial conditions for solving above equations are: P, P, P - ), and P. And at any time, P. Similarly, f ) ) / d. Using equations C-C7 to solve for P ), we can obtain f ) and for holo-cuer HJC interactions. nconveniently, the expressions of the solutions to equations C C7 are so tediously complex to hamper their physical understanding. To get a clean analytical expression for we arbitrarily set and get: + [P] + [P] where P- 6 ) 7 / 6K P - ) + 6 / K P- + [P] 7 / K P-K / K ) + / K ) + [P] / K K ) 7 6 P - K and ) 5 P P- P- P - P - ), K +. This equation is given as Eq. in the main text. As this equation can satisfactorily interpret the [holo-cuer] dependence of fit the holo-cuer data in Figure B to obtain other relevant inetic parameters., we use it to Reference. Xie, X. S.. Single-molecule approach to enzymology. Single Mol. : Xu, W., J. S. Kong, and P. Chen. Single-molecule inetic theory of heterogeneous and enzyme catalysis. J. Phys. Chem. C. in press. S

5 Supporting Figures A 6 B # of Events Figure S. Histograms of HJC trajectories in the absence A) and presence of. μm apo-pbrr69 B). Bin size:.. Each histogram is compiled from more than trajectories # of Events. 7. A 3 B Figure S. Histograms of HJC trajectories in the presence of.5 μm apo-cuer A) and 3 μm apo-cuer B). Bin size:.5. S5

6 9 6 HJC HJC A 3 # of Molecules 8 + μm apo-cuer + μm holo-cuer B C E conf- Figure S3. Histograms of E conf- of HJC A) in the presence of μm apo-cuer B) and μm holo-cuer C). Solid lines are Gaussian fits centered at.59 ±. A),.63 ±. B), and.6 ±. C).. Anisotropy...9 K d.7 ±. μm..5. [apo-cuer] μm) Figure S. Fluorescence anisotropy experiment on Cy-3 labeled double-strand DNA containing only half of the dyad-symmetric sequence 5 -TGACCTTCCCCTTGCTTGGCTTGTT-3, the half sequence is underlined) titrated with apo-cuer. The solid line is the fit using Eq. 5 which gave a K D ~.7 μm. S6

7 Anisotropy [apo-cuer] free, nm [holo-cuer] free, nm Figure S5. Data from Fig. 7 plotted against free protein concentrations. Anisotropy K D.5 ±. μm.7. [apo-cuer] μm) Figure S6. Fluorescence anisotropy experiment on Cy3-labeled HJC titrated with apo-cuer. The solid line is the fit using Eq. 5 giving a K D ~.5 μm which is in between the affinity of apo- CueR to conf- and to conf- of HJC determined from single-molecule measurements. S7