Supplementary Data Computer simulations A Monte Carlo…

Supplementary Data

Computer simulations

          A Monte Carlo approach was employed to simulate the movement of FtsK

particles on  DNA. Each run encompassed the following steps: (1) an FtsK particle

binds randomly to  DNA; (2) FtsK starts moving in either direction with equal

probability; (3) Upon encounter of an FRS in the non-permissive orientation, FtsK

reverses translocation direction with a probability pFRS; (4) The sequence-independent

stochastic reversibility of the FtsK motor was simulated by assuming that FtsK had a

probability p0 = 0.001 (see below) of turning around at each translocation step; (5) Upon

encounter of any of the ends of  DNA, FtsK pauses with a probability of 95% or

reverses translocation direction with a probability of 5% per time step; (6) the event ends

when the pause on one end of  DNA was longer than 10 time steps. The distribution and

orientation of FRS correspond to those naturally occurring on  DNA. Following these

rules, a trace of the position of FtsK versus time was obtained. This process was repeated

2500 times, and mean burst sizes were calculated as for the experimental translocation

traces.

          For pFRS = 0.4 (as determined by Levy et al.1), the burst sizes distribution was

asymmetric (Supplementary Fig. 2B), with bursts in the permissive direction being more

likely than those in the non-permissive one. The total distance traveled by FtsK particles

in the permissive direction was ~70% of the total distance translocated. The net distance

translocated was in the permissive direction in 88% of events.         By repeating this

simulation for other values of pFRS we found that values lower or higher than pFRS = 0.4

did not reproduce well the experimental burst size distribution for FtsK50C.
The lack of sequence recognition by FtsK50C particles was simulated by assuming that

FtsK had a probability p0 of turning around at each translocation step. The burst size

distribution that best represented the experimental data was obtained for p0 = 0.001. In

this case, the burst size distribution was symmetric and thus the probability of a given

burst size was independent of the translocation direction (Supplementary Fig. 2B). Here,

long bursts spanning the whole length of  DNA were as frequent as in the experimental

size distribution. The distance traveled by FtsK particles in the permissive direction was

~50% of the total and net distances translocated. By repeating this simulation for other

values of p0 we found that values lower or higher than p0 = 0.001 did not reproduce the

experimental burst size distribution for FtsK50C.



       Thus, our experimental results can be computationally predicted by assuming that

the probability of turn around by FtsK50C when encountering an FRS is ~40% and that

FtsK50C turns around stochastically without sequence recognition.



The FtsK motor turns around without sequence recognition

       FtsK reverses stochastically in the absence of its FRS recognition domain (Fig.

1B and 2C). The burst size distribution of FtsK50C allows us to measure the FtsK motor

domain's intrinsic processivity, defined as the mean distance translocated in a burst.

Since the translocation of FtsK50C is unaffected by FRS, the burst size distribution is

expected to decay following a Poissonian distribution. The best fit to the FtsK50C

experimental burst size distributions gave a mean processivity of ~9 kbp (Supplementary

Fig. 2C, solid black lines). This mean processivity of FtsK50C is consistent with our
magnetic tweezers experiments (data not shown). Previous processivity measurements for

FtsK50C2 (~ 6.5 kbp) are consistent with our results, but may be lower due to non-specific

-domain/DNA interactions. Our measured processivity is significantly shorter than

distances FtsK translocates during chromosome dimer resolution (~ 250 kbp3). This

propensity of the motor to turnaround every ~9 kbp may have necessitated the evolution

of a mechanism that recognizes the natural distribution of FRS (every ~ 3.5 kbp). This

mechanism ensures FtsK directional movement and may provide a rationale for the

evolution and/or maintenance of the high density of FRS along the chromosome.


Interpretation of DNA looping in the magnetic tweezers assay

       To loop DNA, FtsK must establish two points of contact. While translocating one

DNA fragment, FtsK needs to be anchored to either another region of the same DNA

molecule or a static surface. In this paper, we show that the binding of the -domain to

DNA is not required for anchoring to DNA, as looping is still observed for FtsK50C.

       Looping of DNA by FtsK could be interpreted in terms of an FtsK complex that

translocates DNA while remaining anchored to the surface of the capillary or the bead.

Our optical tweezers experiments4 showed that FtsK particles loop from any location on

DNA, in disagreement with this model.

       Here, we favor a model (with some similar elements to that previously proposed2)

in which an FtsK complex is formed by two coupled motors. Initially, the complex binds

to DNA and one active motor translocates on DNA without looping. At some position on

the DNA tether, one motor binds DNA and remains fixed to it; translocation by the other

motor thus generates a DNA loop. In the absence of FRS, FtsK binds to any DNA

sequence with equal probability. Because of the physical constraint imposed by the
surface of the capillary and bead, the FtsK complex is often localized to the extremity of

the DNA, consistent with the frequently observed full-length translocation events. In the

presence of FRS, however, one of the motors preferentially anchors close to the position

of FRS due to -domain/FRS interactions. In this model, pauses at the location of the FRS

repeat are related to simultaneous specific interactions of FtsK with FRS and non-specific

interactions with the bead or the surface.



       In our experiments, we measure pauses and reversals at specific extensions that

correlate to the position of the FRS repeat. Both proposed models for DNA looping imply

that those pauses and translocation direction reversals result from direct interactions

between FRS and FtsK that are -domain specific.



Translocation of FtsK50C and FtsK50C on DNAno-FRS

       The DNA tether DNAno-FRS did not contain any FRS sequence. Other DNA tethers

(DNAFRS,1/2 and DNAFRS,1/3) contained only a repeat of three FRS sequences in positions

corresponding to 1/2 or 1/3 of the tether length, respectively.

       To test the specificity of the FtsK/FRS interaction, we shortened one end of

DNAFRS,1/2 to create DNAFRS,1/3. In this case, the position of the pauses and translocation

direction reversals representing interactions between FRS and FtsK shifted from ~2 µm

(position of the FRS repeat in DNAFRS,1/2) to ~0.9 µm, the position of the FRS repeat in

the new DNA tether (Supplementary Fig. 3A).

       On a substrate containing no FRS repeat (DNAno-FRS), FtsK50C and FtsK50C

behave similarly: frequent loops the size of the full length of the DNA tether are observed
and pausing behavior is infrequent and non-sequence specific (Supplementary Fig. 3B

and C, respectively).




Supplementary References


1.     Levy, O. et al. Identification of oligonucleotide sequences that direct the
       movement of the Escherichia coli FtsK translocase. Proc Natl Acad Sci U S A
       102, 17618-23 (2005).
2.     Saleh, O.A., Perals, C., Barre, F.X. & Allemand, J.F. Fast, DNA-sequence
       independent translocation by FtsK in a single-molecule experiment. Embo J 23,
       2430-9 (2004).
3.     Corre, J. & Louarn, J.M. Extent of the activity domain and possible roles of FtsK
       in the Escherichia coli chromosome terminus. Mol Microbiol 56, 1539-48 (2005).
4.     Pease, P.J. et al. Sequence-directed DNA translocation by purified FtsK. Science
       307, 586-90 (2005).